Question

Determine if the series

\[\sum_{n=1}^{\infty}n/e^{n} \]

is convergent using the comparison or integral test.

I used the integral test and got -1 + 2/e by computing the integral. Did I select the right test and answer this question correctly?

Answer 1

converges for sure

Answer 2

and integral test works nicely here since
\[\int\frac{xdx}{e^x}=-(x+1)e^{-x}\] and so
\[\int_1^{\infty}\frac{xdx}{e^x}\] is finite