What is the sum from n=0 to infinity of (i^n)/(3^n) ?

The sum from n=0 to infinity of (i^n)/(3^n) is converges

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sum from n=0 to infinity of (i^n)/(3^n)

n = 0 \sum \infty \frac{i ^{n}}{3 ^{n}}

converges

Solution steps

i = 0 \sum \infty \frac{n ^{i}}{3 ^{i}}

n \to \infty lim (n (\frac{\frac{i ^{n}}{3 ^{n}}}{\frac{i ^{n + 1}}{3 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

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What is the sum from n=0 to infinity of (i^n)/(3^n) ?
The sum from n=0 to infinity of (i^n)/(3^n) is converges