Show Limit Theorem: Sum of Sequence is L

[economist1985]

Homework Statement

Suppose that a_n->L as n->infinity. Show that (a1+a2+...+an)/n=L as well.

Homework Equations

The Attempt at a Solution

I'm thinking something about limit theorems here?

 

[boombaby]

use the definition. note that |(a1+a2+...+an)/n-L| = |((a1-L)+...+(an-L))/n|, and I guess you know something about the behavior of |a_n-L| when n goes to infinity :)
hope this helps u

 

[economist1985]

Sheesh, should have seen that. Thanks!

 

[Dick]

Sheesh, should have seen that. Thanks!

No, you shouldn't have seen that. That's not a proof at all. You need to go back to epsilons and deltas for this one.