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Infinite Series Problem
01-07-2016, 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/(1-r) = -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)^(k-1). I've tried it various ways and can never get the result -36/7.

Any ideas.

C
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01-07-2016, 06:07 AM
Post: #2
RE: Infinite Series Problem
Did you try sum() in CAS mode?
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01-07-2016, 06:34 AM (This post was last modified: 01-07-2016 06:35 AM by jte.)
Post: #3
RE: Infinite Series Problem
The CAS currently interprets (-9)(-3/4)^(k-1) as (-9) being given (-3/4)^(k-1) as an argument, not as implicit multiplication of (-9) and (-3/4)^(k-1).

Try using (-9)*(-3/4)^(k-1).
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01-07-2016, 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.
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01-08-2016, 12:01 AM
Post: #5
RE: Infinite Series Problem
(01-07-2016 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)^(k-1),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
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01-11-2016, 05:18 PM
Post: #6
RE: Infinite Series Problem
(01-07-2016 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.
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