Question
Asked Apr 17, 2019
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums (Sn). Then evaluate lim Sn to obtain the value of the series or
state that the series diverges.
n-00
Σ
(2 cot-1(k + 1)-2cot-k)
k-1
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums (Sn). Then evaluate lim Sn to obtain the value of the series or state that the series diverges. n-00 Σ (2 cot-1(k + 1)-2cot-k) k-1

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Expert Answer

Step 1

To find a formula for the nth term of the sequence of partial sums (Sn). Consider the given telescoping series and find some of the terms.

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Step 2

Find the formula for the nth partial sum as follows.

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Step 3

Evaluate the limit of Sn as n t...

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