#### Answer

FALSE

#### Work Step by Step

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 inconclusive when limit =1 .
Hence, the statement is false.