Does the Limit of Sample Expectations Equal the Limit of x_m?

[Jekertee]

Given lim x_m=n
Prove that lim (expectation of samples x_i [with i=[1,m]]) = n too
Thank you

 

[Token]

EDIT: Solution removed

 

[neutrino]

Welcome to PF, Token.

I gather that you might not be familiar with the guidelines of the forum, especially for homework help. Please don't post complete solutions for homework problems.

https://www.physicsforums.com/showthread.php?t=5374

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.

 

[Jekertee]

Thanks for the try, Token, if you has made more posts on PF,
I am not sure if there were a lot of people online when you posted the solution also , . Classic!

 

[Jekertee]

I found the solution for my own, not really waiting for anyone's solution alone,
I use definition of limit to start, then apply the inequality.