Find all complex numbers such that the series

converges.

We can write

This is a geometric series, and so converges absolutely for which implies , and diverges for .

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Stumbling Robot

A Fraction of a Dot
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Find all *z* such that the series *z*^{n} / 3^{n}

Find all complex numbers such that the series

converges.

We can write

This is a geometric series, and so converges absolutely for which implies , and diverges for .