Answer
$0$
Work Step by Step
A sequence is said to be converged if and only if $\lim\limits_{n \to \infty}a_{n}$ is a finite constant.
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}\frac{9^{n+1}}{10^{n}}$
$=\lim\limits_{n \to \infty}9\times (\frac{9}{10})^{n}$
Since, $\lim\limits_{n \to \infty}a^{n}=0$ for $|a|\lt 1$
Thus,
$\lim\limits_{n \to \infty}9\times (\frac{9}{10})^{n}=9\times 0=0$
Hence, the given sequence converges to $0$.
