Series $\sum \frac{n.2^n}{n^n}$ is-

Explanation

$\sum \frac{n.2^n}{n^n}$ putting n = 1, 2, 3, ............ $\sum \frac{n.2^n}{n^n} = 2, 2, \frac{24}{27}, \frac{1}{4}, ..............$ (which are in decreasing order) Hence the series is convergent.