Analysis problem (sequences)--please help

philosophking

Here is the definition:

t_n = [s_1 + s_2 + ... + s_n] / n ; n >/= 1

I have to show that if lim n-> [infinity] s_n = s, then lim n-> [infinity] t_n = s

First of all, I don't think it's true. Because if s is finite, then lim s/n as n-> [infinity] would be zero, right? And thus lim t_n as n-> [infinity] is zero, and they're not the same.

I'm just wondering how to go about this problem. Thank you.

Hurkyl

I think I would try it directly with the epsilon-delta definition of a limit.


BTW, you should be able to convince yourself that the limit of t_n is not always zero by considering a simple example.