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Math Help - Limit of an average

  1. #1
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    Limit of an average

    Given lim(j -> inf)a_j = L, prove lim(j -> inf) (a_1 + a_2 + ... + a_j)/j = L

    I'm really not sure what to do here. Induction won't work, because the claim fails if j is finite. And I'm not sure how to get the lim sup and lim inf. Thoughts? Suggestions?
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  2. #2
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    Re: Limit of an average

    Quote Originally Posted by phys251 View Post
    Given lim(j -> inf)a_j = L, prove lim(j -> inf) (a_1 + a_2 + ... + a_j)/j = L

    I'm really not sure what to do here. Induction won't work, because the claim fails if j is finite. And I'm not sure how to get the lim sup and lim inf. Thoughts? Suggestions?
    That is proved here.
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