prove that $\varlimsup_{n \to \infty} y_n \leq \varlimsup_{n \to \infty} x_n$

Asked Mar 13 '21 at 10:10

Active Mar 13 '21 at 11:04

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$x_n$ is a bounded number sequence and I have a sequence where $y_n = \frac{1}{n}(x_1 + .... + x_n), n \in \mathbb{N}$

I need to prove that $\varlimsup_{n \to \infty} y_n \leq \varlimsup_{n \to \infty} x_n$

Can anybody help me with the proof?

edited Mar 13 '21 at 11:04

asked Mar 13 '21 at 10:10

reameesmehis

https://math.stackexchange.com/a/393926/42969, https://math.stackexchange.com/a/411588/42969 – Martin R Mar 13 '21 at 10:18
I think in the title those limits should be on $n$, not $x$. – Gerry Myerson Mar 13 '21 at 10:57
Yes, thank you, fixed it now – reameesmehis Mar 13 '21 at 11:04

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