#### Answer

TRUE

#### Work Step by Step

$\lim\limits_{n \to \infty}\frac{a_{{n+1}}}{a_{n}}\lt 1$
For this to be true, $a_{n}$ must be decreasing.
$a_{n+1}\lt a_{n}$ and since $a_{n}=0$, then $\lim\limits_{n \to \infty}a_{n}=0$ must be true because while $a_{n}$ is decreasing, it cannot go to exactly or below $0$.
Hence, the statement is true.