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Major Error on Calculator involving Series
02-26-2016, 02:47 PM
Post: #1
Major Error on Calculator involving Series
I'm not sure if anyone is aware of this error regarding infinite series.

For instance:
The sum from 1 to infinity of
(-1)^(n+1) / n^2 should be pi^2/12
However, my calculator returns an answer of -pi^2/12. Even if I approximate this value, I receive -0.82246...

I am using the mobile version of the HP Prime for reference. I have the actual calculator as well, but I'm at work currently, and my calculator is at my apartment.

Also, (-1)^n / n^2 also returns -pi^2/12, which is in fact correct.

Is this something I just have to live with? I teach Calculus II and Differential Equations currently and I am involved in a unit where I am covering infinite series.

Thanks for any help regarding this matter.
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02-26-2016, 04:04 PM
Post: #2
RE: Major Error on Calculator involving Series
My calculator (firmware 8151) also returns -pi^2/12 in CAS mode.

In HOME, using a large number instead of infinity, the calculator returns the correct answer 0.82224...
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02-26-2016, 04:07 PM
Post: #3
RE: Major Error on Calculator involving Series
(02-26-2016 04:04 PM)JMB Wrote:  My calculator (firmware 8151) also returns -pi^2/12 in CAS mode.

In HOME, using a large number instead of infinity, the calculator returns the correct answer 0.82224...

Well, that's a problem, then. Hopefully this will be addressed in a future update. Calculators should not return incorrect values.
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02-26-2016, 08:12 PM
Post: #4
RE: Major Error on Calculator involving Series
Thanks for the info. I have now fixed the issue in Xcas source (and geogebra source).
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02-27-2016, 01:46 AM
Post: #5
RE: Major Error on Calculator involving Series
(02-26-2016 08:12 PM)parisse Wrote:  Thanks for the info. I have now fixed the issue in Xcas source (and geogebra source).

2 questions, was this fixed for higher order alternating series as well, like (-1)^(n+1)/n^4, etc?

Also, will this update be included when the firmware is updated?

I teach with this calculator, and I'd like to be as up to date as possible.

Thanks.
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02-27-2016, 06:57 AM
Post: #6
RE: Major Error on Calculator involving Series
With the fix, normal(sum((-1)^(n+1)/n^4,n,1,inf)) returns 7/720*pi^4. I will update Xcas offline today, so that you can make further checks yourself.
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02-27-2016, 08:22 PM (This post was last modified: 02-27-2016 08:24 PM by Tim Wessman.)
Post: #7
RE: Major Error on Calculator involving Series
(02-27-2016 01:46 AM)LCieParagon Wrote:  Also, will this update be included when the firmware is updated?

Hello,

As one of the HP people who participate on this board, let me explain the reason you won't ever receive an "official" bit of information on this until the day any software update is released.

Basically, HP follows the same policy as most large companies. Namely, there are usually only a few people in the entire company that can release any "forward looking statements" such as "when will a product be released, is a problem going to be fixing in a new release, or even that will be a new release". There a plenty of reasons for this including potential legal trouble (someone sues because they were harmed in some way by a product not having feature X on Y date), people feeling like the company lied about something and the bad PR that can generate, or that something comes up needing to be dealt with immediately that causes delay. Due to these and many other reasons, most companies just don't announce things until they are good and ready.

What that means is that if anyone ever tells you that a release will happen on a certain day, or that a certain feature will be in there, chances are you should not pay attention to them. Since they will not be an official spokesperson (the calc group is just too small a part of the overall HP we would never blip on the larger radar of the time required to address such minor things), chances are they really don't know.

All we are really allowed to say is something like, "We are investigating the issue for potential possible inclusion in a future release". That being said, Prime does include some components that are not exclusive to the HP code - the CAS being the largest most visble one. If the CAS author has put in a fix for a known calculation, the chances of it not being included in a hypothetical future release are very slight. We do try to track very closely the main CAS source to avoid potential problems.

Can I say then that it will be in the next release? No. I cannot even ever say that there will ever be ANY future release. That sort of statement would not be allowed. I could say that should there be any future releases, the chances that this would be in there would be high due to the tracking of the CAS source closely.

Make sense?


I think that the HP calculator group is probably more open and responsive then any other major calculator manufacturer at this point in time precisely because they DO allow direct communication from developers and internal teacher development people within the limits that have been set. There are quite a few new features, fixes, or suggestions in Prime that can be directly traced back to posts like yours on a board such as this in every release that has happened so far.

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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02-28-2016, 03:14 PM
Post: #8
RE: Major Error on Calculator involving Series
(02-27-2016 08:22 PM)Tim Wessman Wrote:  I think that the HP calculator group is probably more open and responsive then any other major calculator manufacturer at this point in time precisely because they DO allow direct communication from developers and internal teacher development people within the limits that have been set. There are quite a few new features, fixes, or suggestions in Prime that can be directly traced back to posts like yours on a board such as this in every release that has happened so far.

Where is the "Like" button? Your support is very much appreciated.

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02-28-2016, 04:24 PM
Post: #9
RE: Major Error on Calculator involving Series
(02-28-2016 03:14 PM)Marcus von Cube Wrote:  
(02-27-2016 08:22 PM)Tim Wessman Wrote:  I think that the HP calculator group is probably more open and responsive then any other major calculator manufacturer at this point in time precisely because they DO allow direct communication from developers and internal teacher development people within the limits that have been set. There are quite a few new features, fixes, or suggestions in Prime that can be directly traced back to posts like yours on a board such as this in every release that has happened so far.

Where is the "Like" button? Your support is very much appreciated.

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02-28-2016, 06:58 PM
Post: #10
RE: Major Error on Calculator involving Series
(02-27-2016 08:22 PM)Tim Wessman Wrote:  
(02-27-2016 01:46 AM)LCieParagon Wrote:  Also, will this update be included when the firmware is updated?

Hello,

As one of the HP people who participate on this board, let me explain the reason you won't ever receive an "official" bit of information on this until the day any software update is released.

Basically, HP follows the same policy as most large companies. Namely, there are usually only a few people in the entire company that can release any "forward looking statements" such as "when will a product be released, is a problem going to be fixing in a new release, or even that will be a new release". There a plenty of reasons for this including potential legal trouble (someone sues because they were harmed in some way by a product not having feature X on Y date), people feeling like the company lied about something and the bad PR that can generate, or that something comes up needing to be dealt with immediately that causes delay. Due to these and many other reasons, most companies just don't announce things until they are good and ready.

What that means is that if anyone ever tells you that a release will happen on a certain day, or that a certain feature will be in there, chances are you should not pay attention to them. Since they will not be an official spokesperson (the calc group is just too small a part of the overall HP we would never blip on the larger radar of the time required to address such minor things), chances are they really don't know.

All we are really allowed to say is something like, "We are investigating the issue for potential possible inclusion in a future release". That being said, Prime does include some components that are not exclusive to the HP code - the CAS being the largest most visble one. If the CAS author has put in a fix for a known calculation, the chances of it not being included in a hypothetical future release are very slight. We do try to track very closely the main CAS source to avoid potential problems.

Can I say then that it will be in the next release? No. I cannot even ever say that there will ever be ANY future release. That sort of statement would not be allowed. I could say that should there be any future releases, the chances that this would be in there would be high due to the tracking of the CAS source closely.

Make sense?


I think that the HP calculator group is probably more open and responsive then any other major calculator manufacturer at this point in time precisely because they DO allow direct communication from developers and internal teacher development people within the limits that have been set. There are quite a few new features, fixes, or suggestions in Prime that can be directly traced back to posts like yours on a board such as this in every release that has happened so far.

Thank you Tim and the rest of the HP calc group for your support! I appreciate it!
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02-29-2016, 01:16 AM
Post: #11
RE: Major Error on Calculator involving Series
(02-27-2016 08:22 PM)Tim Wessman Wrote:  
(02-27-2016 01:46 AM)LCieParagon Wrote:  Also, will this update be included when the firmware is updated?

Hello,

As one of the HP people who participate on this board, let me explain the reason you won't ever receive an "official" bit of information on this until the day any software update is released.

Basically, HP follows the same policy as most large companies. Namely, there are usually only a few people in the entire company that can release any "forward looking statements" such as "when will a product be released, is a problem going to be fixing in a new release, or even that will be a new release". There a plenty of reasons for this including potential legal trouble (someone sues because they were harmed in some way by a product not having feature X on Y date), people feeling like the company lied about something and the bad PR that can generate, or that something comes up needing to be dealt with immediately that causes delay. Due to these and many other reasons, most companies just don't announce things until they are good and ready.

What that means is that if anyone ever tells you that a release will happen on a certain day, or that a certain feature will be in there, chances are you should not pay attention to them. Since they will not be an official spokesperson (the calc group is just too small a part of the overall HP we would never blip on the larger radar of the time required to address such minor things), chances are they really don't know.

All we are really allowed to say is something like, "We are investigating the issue for potential possible inclusion in a future release". That being said, Prime does include some components that are not exclusive to the HP code - the CAS being the largest most visble one. If the CAS author has put in a fix for a known calculation, the chances of it not being included in a hypothetical future release are very slight. We do try to track very closely the main CAS source to avoid potential problems.

Can I say then that it will be in the next release? No. I cannot even ever say that there will ever be ANY future release. That sort of statement would not be allowed. I could say that should there be any future releases, the chances that this would be in there would be high due to the tracking of the CAS source closely.

Make sense?


I think that the HP calculator group is probably more open and responsive then any other major calculator manufacturer at this point in time precisely because they DO allow direct communication from developers and internal teacher development people within the limits that have been set. There are quite a few new features, fixes, or suggestions in Prime that can be directly traced back to posts like yours on a board such as this in every release that has happened so far.

This is fine and all, but like I have said, I have concerns as well. This calculator was approved for use by the College Board. My students plan on taking the AP test, and as such, are allowed to use this device on certain sections. My students can potentially receive incorrect responses by recording incorrect responses that your product displays.

While I do like this calculator very much and plan to use it for the foreseeable future, this can be detrimental to a student taking an exam utilizing this device. I find it troubling that students quite possibly may be penalized for faulty technology that is approved for use.

An example where a student can receive this question wrong on a test would be in calculating the remainder on infinite, alternating series which College Board now tests.

As an educator, I always enjoy learning myself, and if I'm proven wrong, I am happy to admit my mistakes.

Additionally, no where in my post have I compared competitors' products to yours. I find your response in regards to that curt, and unnecessary. Furthermore, your response didn't illicit a "Like" as it has with other members on this forum.
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02-29-2016, 01:55 AM (This post was last modified: 02-29-2016 01:58 AM by Tim Wessman.)
Post: #12
RE: Major Error on Calculator involving Series
(02-29-2016 01:16 AM)LCieParagon Wrote:  This is fine and all, but like I have said, I have concerns as well. This calculator was approved for use by the College Board. My students plan on taking the AP test, and as such, are allowed to use this device on certain sections. My students can potentially receive incorrect responses by recording incorrect responses that your product displays.

I do understand your point of view. Unfortunately, no product of the complexity of a modern CAS calculator can possibly be bug free simply because symbolic mathematics is very, very hard for computers to do. No matter how well written the program, they can't think like the marvelous human brain.

The College Board recognizes that bugs can and will happen, yet they still require their use for AP calculus in that section. In fact, I know there was quite a bit of an uproar ~2 years back or so when two allowed products from one of our competitors has a CAS bug that caused a large percentage of students to get an incorrect result in the middle of a question and were ultimately penalized because of it (they received credit for the proper process and steps, but did indeed lose partial credit due to that technology error).

Quote:While I do like this calculator very much and plan to use it for the foreseeable future, this can be detrimental to a student taking an exam utilizing this device. I find it troubling that students quite possibly may be penalized for faulty technology that is approved for use.

I do agree that it is troubling. Unfortunately, the way the tests are designed right now does penalize for an error in the technology. I spent quite a bit of time talking with some of the chief AP calc readers around this subject at last year's NCTM and ultimately what was the unanimous opinion there was that a) students can lose credit for errors not their own, and b) yet even despite that, the benefits outweigh the negatives.

The HP calculator group is always conscious regarding testing deadlines (not just here in America, but around the world) and tries to plan accordingly. I was simply explaining why nobody would be able to answer your part of the question regarding "when might this be fixed". I simply can't make those announcements.

Quote:Additionally, no where in my post have I compared competitors' products to yours. I find your response in regards to that curt, and unnecessary. Furthermore, your response didn't illicit a "Like" as it has with other members on this forum.

I can understand your point of view here and respect it. My intent was not trying to compare competitors, rather highlighting that ALL do the same thing with respect to this type of communication (not discussing when stuff will be fixed or launched).

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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02-29-2016, 04:06 AM (This post was last modified: 02-29-2016 05:30 PM by Han.)
Post: #13
RE: Major Error on Calculator involving Series
I am not an employee for HP nor any company that makes calculators, nor any group associated with the college board or AP exams. I do teach mathematics, however, and encourage students to take advantage of whatever technology is available to them (whether it be a scientific or graphing calculator, or programs such as Maple, Mathematica, Matlab, etc). In fact, I love technology and enjoy finding ways of incorporating it into the classroom. When I was in high school, calculators were a novelty. Nowadays, even toddlers know how to use cell phones and tablets. I see technology as yet another means to connect with students who may not have been as interested in learning mathematics without technology. Now, with that out of the way...

Technology in the classroom, in my opinion, should always be used as a means for getting answers more quickly, as opposed to simply getting the answers. No matter how well a calculator is programmed, it will never be 100% mathematically correct. In fact, even with the most powerful hardware, calculators are limited by... well, their hardware. For example, when one graphs \( sin(ax) \) where \( a \) is a large value, the graph (on any calculator or even computer) will be wrong for sufficiently large \( a \) simply because the pixel density will eventually be insufficient if the frequency in the graph is high enough that several peaks or valleys of the sinusoidal graph occur within the width of one single pixel. And graphing is one of the most basic features of graphing calculators. I am of the opinion that this bug will never be completely eradicated since screens will always be physically limited by the number of pixels it can display.

If students are losing substantial amounts of points due to errors in their calculator, then the first issue is not the calculator. I would question whether students properly learned the mathematics needed for the problem as opposed to having simply learned how to use a calculator to get answers. There is a huge difference between learning, say, calculus and its principles and learning how to use a few commands to solve calculus problems. The former would enable students to at least have a strong suspicion that their calculator is giving them the wrong answer.

Consider the hypothetical (but very possible, as I have seen many such cases) example of a student who has poor mathematical skills that would normally prevent him from correctly computing a derivative (poor algebraic skills, or improperly applying various derivative rules). With a calculator that has a computer algebra system, he would be able to overcome that deficiency and solve optimization problems. So on the one hand, he can properly demonstrate that he is capable of solving applications that require derivatives, but on the other hand, he can only do so with a crutch. I have seen a very large number of students (over the course of many years, though) who regularly butcher a simple question of "find the derivative of the following function(s)" and yet can give me the precise sequence of steps of solving optimization problems -- including the proper definitions of terms such as "critical points" and "concavity" as well as properly explain what derivatives are and how they are computed and used, etc. It seems quite reasonable to consider such a student as having mastered optimization (provided he have a calculator as a "crutch"). And in the real world, knowing how to compute a derivative by hand would more often be atypical than not. So the deficiency does not really hinder him out in the real world. On the other hand, one could argue that the student has not mastered being able to apply appropriate derivative rules to compute a derivative. So if he cannot compute derivatives, one might question his ability to solve any problems involving derivatives.

Since I teach with technology, I find myself constantly reminding my students that technology is a man-made tool. Since man will always make mistakes, they must not rely on their tools to the point of not being able to discern whether the tools are working properly.

You may find this article an interesting read about a bug in Mathematica (which is an expensive commercial package): When a computer algebra system gives the wrong answers

Within the article is also a link to The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?

Again, I would like to emphasize that the bug is not only known, but has not been addressed fully, and exists in a commercial product that costs a lot of money -- and that real-world professionals rely on for their research.

Quote:Additionally, no where in my post have I compared competitors' products to yours. I find your response in regards to that curt, and unnecessary. Furthermore, your response didn't illicit a "Like" as it has with other members on this forum.

I respectfully disagree. The comparison actually had nothing to do with competitor's products as you suggest; Tim was talking about practices used by HP and its competitors with respect to communication with their respective consumers. I think the practice of open discussion with consumers and even heeding the advice (in the form of feature requests) of consumers shows that the HP calculator group has a sincere approach to making this calculator as great as it can be.

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02-29-2016, 05:55 AM
Post: #14
RE: Major Error on Calculator involving Series
(02-29-2016 04:06 AM)Han Wrote:  
In fact, even with the most powerful hardware, calculators are limited by... well, their hardware. For example, when one graphs \( sin(ax) \) where \( a \) is a large value, the graph (on any calculator or even computer) will be wrong for sufficiently large \( a \) simply because the pixel density will eventually be insufficient if the frequency in the graph is high enough that several peaks or valleys of the sinusoidal graph occur within the width of one single pixel. And graphing is one of the most basic features of graphing calculators. I am of the opinion that this bug will never be completely eradicated since screens will always be physically limited by the number of pixels it can display.
Han, you might want to try the Advanced Graphing app and look at
http://www.dgp.toronto.edu/~mooncake/pap...Tupper.pdf

A problem with most automated graphing techniques is not they can be wrong, but that they cannot be right as there is no precise definition of what their output means. (Or is supposed to mean: what can one infer of the mathematical relation, given the image shown by the device?) A strict interpretation that remains understandable to those not versed in the intricate details of the construction and limitations of the typical techniques employed is that: this is the output of the algorithm. (Which isn't very revealing…) There are techniques that allow for some information to be revealed by a computer-generated image. (E.g.,: this pixel is black -> there is a point in the Cartesian region the point represents that belongs to the relation being graphed. An implementation that could satisfy such requirements, if it uses floating-point, must keep track of things like round-off and properties of the function(s) being evaluated.)

The Advanced Graphing app takes some steps towards addressing the shortcomings you mention. Some additional steps remain to be taken.
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02-29-2016, 05:29 PM
Post: #15
RE: Major Error on Calculator involving Series
(02-29-2016 05:55 AM)jte Wrote:  
(02-29-2016 04:06 AM)Han Wrote:  
In fact, even with the most powerful hardware, calculators are limited by... well, their hardware. For example, when one graphs \( sin(ax) \) where \( a \) is a large value, the graph (on any calculator or even computer) will be wrong for sufficiently large \( a \) simply because the pixel density will eventually be insufficient if the frequency in the graph is high enough that several peaks or valleys of the sinusoidal graph occur within the width of one single pixel. And graphing is one of the most basic features of graphing calculators. I am of the opinion that this bug will never be completely eradicated since screens will always be physically limited by the number of pixels it can display.
Han, you might want to try the Advanced Graphing app and look at
http://www.dgp.toronto.edu/~mooncake/pap...Tupper.pdf

A problem with most automated graphing techniques is not they can be wrong, but that they cannot be right as there is no precise definition of what their output means. (Or is supposed to mean: what can one infer of the mathematical relation, given the image shown by the device?) A strict interpretation that remains understandable to those not versed in the intricate details of the construction and limitations of the typical techniques employed is that: this is the output of the algorithm. (Which isn't very revealing…) There are techniques that allow for some information to be revealed by a computer-generated image. (E.g.,: this pixel is black -> there is a point in the Cartesian region the point represents that belongs to the relation being graphed. An implementation that could satisfy such requirements, if it uses floating-point, must keep track of things like round-off and properties of the function(s) being evaluated.)

The Advanced Graphing app takes some steps towards addressing the shortcomings you mention. Some additional steps remain to be taken.

The Advanced Graphing app is indeed a huge leap in the right direction (your linked article was also very informative). It is also amazingly fast.

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02-29-2016, 08:34 PM
Post: #16
RE: Major Error on Calculator involving Series
jte: Thanks for the interesting paper re graphing!
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03-06-2016, 01:52 PM
Post: #17
RE: Major Error on Calculator involving Series
LCieParagon Wrote:This is fine and all, but like I have said, I have concerns as well. This calculator was approved for use by the College Board. My students plan on taking the AP test, and as such, are allowed to use this device on certain sections. My students can potentially receive incorrect responses by recording incorrect responses that your product displays.

I look forward to that bug being fixed as well.

For what it's worth, the College Board AP tests never ask any questions that require a CAS. I tell my AP Calc students that if they find themselves needing the CAS on the AP exam, then they're probably doing it wrong. The type of question in which a CAS would be an advantage typically shows up on the non-calculator sections.

That said, not all exams are AP exams. The bug does need to be fixed. I see that GeoGebra, which also uses xcas, used to give the wrong answer but now gives the right answer, so that looks promising.

For reference, the exam that Tim mentioned was the 2013 AP Calc AB Exam (http://media.collegeboard.com/digitalSer...lus_ab.pdf). Question 2a wreaked havoc with anybody who had a TI Nspire CAS or TI-89 and tried to solve by using |v(t)|=2. Anyone with a non-CAS calculator was fine. The numeric answer was only worth 1 point, but it locked up the calculator to the point that kids had to reset or pull a battery. What was really lost was time and mental focus.


LCieParagon Wrote:Additionally, no where in my post have I compared competitors' products to yours. I find your response in regards to that curt, and unnecessary. Furthermore, your response didn't illicit a "Like" as it has with other members on this forum.

I don't usually weigh in to things like this, but my first thought was "Whoa, did we read the same post?" The reason people "liked" it so much is because it was such a clear, concise, and patient response from a company person that actually knows about the product and is involved in its developement --- highly uncharacteristic in this day and age. Now that a week has passed, go back and read it again. Maybe it will read differently this time.

All the best to your students in May.
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03-07-2016, 09:05 AM
Post: #18
RE: Major Error on Calculator involving Series
I am also in some trouble with the Prime at school.
I had to choose between Prime, Texas and Casio for my students, I choosed the Prime because I find it better to use as nspire-cas and class-pad.

Now I am working with my students with complex numbers and it turns out that in home the Prime does not give the correct answer if you calculate the square root of a complex number when both the real and imaginary part are negatives.
This is quite bad, because if the students calculate it they will find a wrong result.
The fact that the Prime can not compute Riemann Zeta function for complex values is not so bad, you do not receive an answer, no problem.
The problem in when you do a calculation and the calculator gives you a wrong answer.

I am a former electronic engineer and I wrote a lot of software for complex telecommunication devices, so i know very good what it means to write, debug and release a software. I am not criticizing the work done by HP, I know they did a great job.

But still I can not give my students a calculator which gives wrong answers, they use it in the tests we do in the classroom and they will go at the exams with it...

So now I have to decide if next year I can still propose the HP Prime to the new students or if I have to change it. I still find the Prime a very good calculator, I like it and I will continue to use it, but the students are still learning math so they need a calculator that always gives correct answers.

I will decide in august what I will do...

Thank you to all for the work done !!!
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03-07-2016, 10:56 AM
Post: #19
RE: Major Error on Calculator involving Series
This has been discussed before, http://www.hpmuseum.org/forum/thread-5744.html, and I think I remember reading elsewhere, that there was a fix for it, possibly for the next firmware release.

For some reason, the search feature doesn't seem to be working on this forum, this morning.

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03-07-2016, 11:59 AM
Post: #20
RE: Major Error on Calculator involving Series
I know it has already been discussed, and as you say, we come back to the next firmware release.

It seems like it has already been corrected in the mobile version, but smartphones are not allowed during the exams...
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