Ratio Test for Convergence Practice Test

Diverges because $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=1$.

Inconclusive because $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=e$.

Diverges because $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=\frac{1}{e}<1$.

Converges because $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=1$.

Converges because $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|=\frac{1}{e}<1$.