Question 24
Consider the sequence $\left(a_{n}\right)_{n=1}^{\infty}$, $a_{n}=\underbrace{11 \ldots 1}_{n \text{ digits }}\underbrace{88 \ldots 8}_{n \text{ digits }}$, $\forall n \geq 1$. Compute $\lim _{n \rightarrow \infty}\left\{\sqrt{a_{n}}\right\}$, where $\{t\}$ denotes the fractional part of the number $t$.