$\lim_{n\to \infty} \sqrt n(A_{n+1}-A_n) $ when $ A_n = \frac{1}{n}(a_1+a_2+\cdots+a_n)$ and $|a_n| \leq 1$
Compute: $\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ where $A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n)$