I have tried to compute the radius of convergence for the following series: $$\sum\limits_{n=0}^{\infty}ni^nz^n$$ but I keep getting $zi$ as the limit when I take the ratio.
What is the correct method for this problem?
2026-04-17 17:53:02.1776448382
Radius of convergence using ratio test complex
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Use the Cauchy Hadamard formula:
$$\frac1R=\lim\sup_{n\to\infty}\sqrt[n]{|ni^n|}=\lim\sup_{n\to\infty}\sqrt[n]n\,|i|=1\implies R=1$$