Find all complex numbers such that the series

converges.

First, we consider

So, by the ratio test, the series converges if and diverges if . If with then the series also converges by Dirichlet’s test. Hence, the series converges for with .

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Stumbling Robot

A Fraction of a Dot
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Find all *z* such that the series *(2z+3)*^{n} / (n log (n+1)) converges

Find all complex numbers such that the series

converges.

First, we consider

So, by the ratio test, the series converges if and diverges if . If with then the series also converges by Dirichlet’s test. Hence, the series converges for with .