If $u_n>0$ and $v_n=\frac{u_1+u_2+…+u_n}{n}$, then show that $\sum v_n$ is divergent.

Question

If $u_n>0$ and $v_n=\frac{u_1+u_2+...+u_n}{n}$, then show that $\sum v_n$ is divergent.

Let $s_n=u_1 +u_2+ \dots +u_n$. Nothing is given about the convergence of $\sum u_n$ and unable to check the convergence of the series $\sum v_n=\sum \frac{s_n}{n}$. I need help.

Answer 1

$v_n > \frac {u_1} n$ so $\sum v_n > \sum \frac {u_1} n =\infty$.