Is the series \sum_(n=1)^\infty n e^(-n) absolutely convergent, conditionally convergent or divergent?

(Use the appropriate test)

1 Answer
Apr 20, 2018

Converges

Explanation:

Apply the ratio test:

lim_(n to oo ) |a_(n+1)/a_n |

= lim_(n to oo ) |((n+1) e^(-(n+1)))/(n e^(-n)) |

= lim_(n to oo ) |((1+1/n) )/( e) | = 1/e lt 1

It converges :)