Find all complex numbers such that the series

converges.

This is a geometric series

Therefore it converge if and only if

Hence, the series converges for all except .

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Stumbling Robot

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

Find all complex numbers such that the series

converges.

This is a geometric series

Therefore it converge if and only if

Hence, the series converges for all except .