Show that if $\sum \limits_{n=1}^\infty a_n$ converges then $\lim\limits_{n\to\infty}\frac{1}{n}\sum _{k=1}^n ka_k=0$
If $\sum_{n=1}^\infty a_n$ converges, prove that $\lim_{n\to \infty} (1/n) \sum_{k=1}^n ka_k = 0$.