Math Help - [SOLVED] Determine if the series converges

1. [SOLVED] Determine if the series converges

the series is $\frac{1}{e^{1/k}}$ with k=1 going to infinity
do i use the divergence test and get my limit as 1 which means the series diverges?

2. Originally Posted by vinson24
the series is $\frac{1}{e^{1/k}}$ with k=1 going to infinity
do i use the divergence test and get my limit as 1 which means the series diverges?

If the series is $\sum^\infty_{k=1}\frac{1}{e^{1/k}}$ , then $\lim_{k\to\infty}\frac{1}{e^{1/k}}=\frac{1}{e^{\lim_{k\to\infty}1/k}}=\frac{1}{e^0}=1\neq 0$ and thus the series can't converge.

Tonio

3. thanks i wanted to make sure i picked the right test