the series is $\displaystyle \frac{1}{e^{1/k}}$ with k=1 going to infinity
do i use the divergence test and get my limit as 1 which means the series diverges?
the series is $\displaystyle \frac{1}{e^{1/k}}$ 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 $\displaystyle \sum^\infty_{k=1}\frac{1}{e^{1/k}}$ , then $\displaystyle \lim_{k\to\infty}\frac{1}{e^{1/k}}=\frac{1}{e^{\lim_{k\to\infty}1/k}}=\frac{1}{e^0}=1\neq 0$ and thus the series can't converge.