Show Limit Theorem: Sum of Sequence is L

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Homework Statement


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


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The Attempt at a Solution


I'm thinking something about limit theorems here?
 
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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
 
Sheesh, should have seen that. Thanks!
 
economist1985 said:
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.
 
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