Infinite Series Problem

01072016, 05:45 AM
Post: #1




Infinite Series Problem
For my Calc III class lecture I have the following infinite series for the students:
9 + 27/4  81/16 + 243/64  729/256 ... This is a geometric series with the first term a = 9 and the common ratio r = 3/4. The infinite series value is S = a/(1r) = 9/(1(3/4)) = 36/7 When entered into the Prime, regardless how I enter it I get the result of +/ inf, not 36/7. I'm entering it as the summation as k goes from 1 to infinity, of (9)(3/4)^(k1). I've tried it various ways and can never get the result 36/7. Any ideas. C 

01072016, 06:07 AM
Post: #2




RE: Infinite Series Problem
Did you try sum() in CAS mode?


01072016, 06:34 AM
(This post was last modified: 01072016 06:35 AM by jte.)
Post: #3




RE: Infinite Series Problem
The CAS currently interprets (9)(3/4)^(k1) as (9) being given (3/4)^(k1) as an argument, not as implicit multiplication of (9) and (3/4)^(k1).
Try using (9)*(3/4)^(k1). 

01072016, 11:32 PM
Post: #4




RE: Infinite Series Problem
So far none of the suggestions have worked, neither with the summation sign, nor the sum command. I think the problem lies with it being an alternating series and the parsing of the parentheses. The prime seems to be ignoring the parentheses around the base (0.75)^k. Non alternating series and partial sums seem to work, but not an infinite alternating series. Still not sure what is actually happening though. Seems a little random on what is evaluated and what is no.


01082016, 12:01 AM
Post: #5




RE: Infinite Series Problem
(01072016 11:32 PM)chazzs Wrote: So far none of the suggestions have worked, neither with the summation sign, nor the sum command. I think the problem lies with it being an alternating series and the parsing of the parentheses. The prime seems to be ignoring the parentheses around the base (0.75)^k. Non alternating series and partial sums seem to work, but not an infinite alternating series. Still not sure what is actually happening though. Seems a little random on what is evaluated and what is no. If you enter Σ(9*(3/4)^(k1),k,1,∞) in (algebraic notation in) CAS you should get the desired result. You can also use textbook and the template and get the same result. The multiplication must be explicit between 9 and (3/4), and as seems to be the case with most CAS functions the Angle Measure setting must be Radians. Hope this helps Cheers, Terje 

01112016, 05:18 PM
Post: #6




RE: Infinite Series Problem
(01072016 11:32 PM)chazzs Wrote: So far none of the suggestions have worked, neither with the summation sign, nor the sum command. Have you been able to resolve this? Indeed, you must put * between things in the CAS to avoid problems as stated. TW Although I work for the HP calculator group, the views and opinions I post here are my own. 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)