Help with Telescoping Series Problem

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Homework Help Overview

The discussion revolves around a telescoping series problem, where participants are attempting to evaluate the series and reconcile differing results. The original poster mentions arriving at an answer of pi/3, while another source suggests -pi/6 as the correct answer.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the behavior of arccos terms in the series and question whether they approach zero. There is an inquiry about how to properly evaluate the partial sum of the series.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the series and how to handle the limits involved. Guidance has been offered regarding evaluating the partial sum and considering limits as N approaches infinity.

Contextual Notes

There are references to specific terms in the series that may not be approaching zero, and participants are considering the implications of this on their calculations. The original problem statement and attempts at solutions are attached but not detailed in the discussion.

student93
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Homework Statement



Problem is attached in this post.

Homework Equations



Problem is attached in this post.

The Attempt at a Solution



Attempt at solution is attached.

Apparently the answer is -pi/6, however I've solved for it several times and keep getting my answer as pi/3 via Telescoping Series
 

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student93 said:

Homework Statement



Problem is attached in this post.


Homework Equations



Problem is attached in this post.

The Attempt at a Solution



Attempt at solution is attached.

Apparently the answer is -pi/6, however I've solved for it several times and keep getting my answer as pi/3 via Telescoping Series

The arccos terms in your telescoping series are not approaching 0. You can't ignore everything after the ... You need to take a limit of the partial sum.
 
Dick said:
The arccos terms in your telescoping series are not approaching 0. You can't ignore everything after the ... You need to take a limit of the partial sum.

How would I go about solving for the partial sum?
 
student93 said:
How would I go about solving for the partial sum?

Telescope the sum up to an upper limit of N instead of infinity. Then take the limit of the result as N->infinity.
 

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