Prove that the following sum converges and has the given value.

First, we need to get the terms in the sum into the form so we can use the theorem on telescoping sums (Theorem 10.4 on page 386 of Apostol).

where . Hence,

Hence,

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Stumbling Robot

A Fraction of a Dot
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Prove that the sum from 1 to ∞ of *1 / (n*^{2} – 1) = 3/4

Prove that the following sum converges and has the given value.

First, we need to get the terms in the sum into the form so we can use the theorem on telescoping sums (Theorem 10.4 on page 386 of Apostol).

where . Hence,

Hence,