Help with Telescoping Series Problem

[student93]

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

 

[Dick]

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.

 

[student93]

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?

 

[Dick]

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.