Find all such that the series

converges and compute the sum.

First, we write

By Theorem 11.9 we know that we can differentiate a power series term-by-term, so we have

valid for (since this was where the geometric series was valid).

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Stumbling Robot

A Fraction of a Dot
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Compute the sum of the series *∑ nx*^{n}

Find all such that the series

converges and compute the sum.

First, we write

By Theorem 11.9 we know that we can differentiate a power series term-by-term, so we have

valid for (since this was where the geometric series was valid).