Provided that $\lim \limits_{n\to \infty} u_n=l$, prove that $\lim \limits_{n\to \infty} \frac{\sum_{k=1}^nu_k}{n}=l$
If $a_k\geq0$ is a decreasing sequence converging to $0$, do we have $\lim_{n\to\infty}\frac{\sum_{k=1}^n a_k}n = 0$?