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 $\lim_{n\to\infty}\dfrac{a_1+a_2+\dots+a_n}{n}=0$?

Use Jensen's inequality, http://en.wikipedia.org/wiki/Jensen%27s_inequality on the real-valued function of real numbers
$$
f(x)=x^4\,.
$$
