I have problem figuring out if this series is convergent or divergent. Please help!
$\sum_{n=1}^{\infty} \frac{1}{\exp(1/n)}$
Thanks
I have problem figuring out if this series is convergent or divergent. Please help!
$\sum_{n=1}^{\infty} \frac{1}{\exp(1/n)}$
Thanks
as n goes to infinity , $ e^{\frac{1}{n}} $ goes to 1. So your limit of summand goes to 1.. Therefore it should be divergent.
I'd use the Divergence Test to show that this infinite series diverges.
The theorem states that if a series ${a_n}$ does not converge to $0$, then $\sum_{n=1}^{\infty} a_{n}$ diverges.
$\lim_{n\to\infty}\frac{1}{e^{\frac{1}{n}}} = \frac{1}{e^0} \to 1 \ne0 \implies a_{n} \ \ \text {diverges}$