Convergence of summable sequences If $(a_n)$ is a sequence such that
$$\lim_{n\to\infty}\frac{a_1^4+a_2^4+\dots+a_n^4}{n}=0.$$
How do I show that $\lim_{n\to\infty}\dfrac{a_1+a_2+\dots+a_n}{n}=0$?

Using CS, you can show, $(\sum_{i} a_i/n)^2\le (\sum_{i}a_i^2/n)$ and similarly $(\sum_{i}a_i^2/n)^2\le (\sum_{i}a_i^4/n)$. So using the given condition the result follows.
