## Calculus: Early Transcendentals 8th Edition

Ratio Test: $\lim\limits_{n \to +\infty}|\frac{a_{n}+1}{a_{n}}|=\lim\limits_{n \to +\infty}\frac{1}{(n+1)^{3}}\times \frac{n^{3}}{1}$ $=\lim\limits_{n \to +\infty}|\frac{1}{(1+1/n)^{3}}|$ $=\frac{1}{(1+1/\infty)^{3}}$ $=\frac{1}{(1+0)^{3}}$ $=1$ Ratio Test fails when limit =1 . Hence, the statement is false.