# Investigate convergence of the series Σ e^n/n^2 from n=1 to ∞ | test the convergence of series Σ e^n/n^2 from n=1 to ∞

\lim_{n\rightarrow \infty}\frac{e^n}{n^2}

## Solution

Calculate the limit \lim_{n\rightarrow \infty}\frac{e^n}{n^2} Using L’Hopital’s rule, we find

\lim_{x\rightarrow \infty}\frac{e^x}{x^2}=\lim_{x\rightarrow \infty}\frac{e^x}{2x}=\lim_{x\rightarrow \infty}\frac{e^x}{2}=\infty

Hence, the original series diverges by the nth term test