- #1
JG89
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Homework Statement
Prove if that if the limit of a_n = c as n approaches infinity, then the limit of o_n = c as n approaches infinity, where o_n is the arithmetic mean (a_1 + ... + a_n)/n
Homework Equations
I can't figure out how to bound it from below.
The Attempt at a Solution
Assuming that the terms go in ascending order, then a_n is the largest term in the numerator, and so o_n <= n(a_n)/n = a_n.
So I have it bounded above. But I can't figure out how to bound it below, such that the sequence which bounds it below converges to a_n as well. Help would be appreciated!