This is a question from the book Methods of Real Analysis by R. R. Goldberg.
If $(s_n)$ is a sequence of real numbers and if $\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$ then prove that: $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$.
I don't have any idea how to start working on this problem. Please help. Thanks.