Answer
Diverges
Work Step by Step
Apply the Ratio test to the Series
$\Sigma^{\infty}_{n=1} n(\frac{6}{5})^n$
$\lim\limits_{n \to \infty} |\frac{(n+1)(\frac{6}{5})^{n+1}}{n(\frac{6}{5})^n}|$
$\lim\limits_{n \to \infty} \frac{6(n+1)}{5n} $
$\lim\limits_{n \to \infty} \frac{6}{5} + \frac{6}{5n} = \frac{6}{5} >1$
Because the answer is greater than 1, the series diverges
