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$\sum_{n=0}^{\infty} \frac{n^n}{3^{1+3n}}$

I have, by Cauchy Criterion

$\lim_{n \rightarrow \infty} \sqrt[n]{|a_n|}= \frac{1}{27} \lim_{n \rightarrow \infty} \frac{n}{3^{1/n}}= ?$

How a finish?

Cheers!

3 Answers 3