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

We simplify the terms and then apply the theorem on sums of telescoping series (Theorem 10.7, page 386 of Apostol),

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Stumbling Robot

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

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

We simplify the terms and then apply the theorem on sums of telescoping series (Theorem 10.7, page 386 of Apostol),