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 ∞ solved problems in calculus

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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

infinite series problems and solutions


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