Question

is the following series convergent? Justify your answers! the sum where n=1 of n/(e^n)

Answer 1

try ratio test

Answer 2

\[\sum_{n=1}^\infty \frac{n}{e^n}\]
Ratio test:
\[\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=\lim_{n\to\infty}\left|\frac{n+1}{e^{n+1}}\cdot\frac{e^n}{n}\right|\]
Find the limit. If it's less than 1, the series converges. If it's greater than 1, it diverges. If it equals 1, try a different test.