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 work...
@MartinSleziak: Rolled back. Those two should be relevant while means is not. — Jack1 min ago
@Jack Thanks for the rollback and also for your attention to tags. I agree that (means) is questionable here. Feel free to ping me here or in chat if you think that these tag-related comments are no longer needed and should be removed. — Martin Sleziak8 secs ago
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 work...
