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Math Help - Big O

  1. #1
    Junior Member
    Joined
    Dec 2008
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    62

    Big O

    Let  N > M . Prove that for  k > 1 ,  \sum_{n=M+1}^{N} n^{-k} = O(M^{-k+1}) as  M \to \infty .
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  2. #2
    Newbie
    Joined
    Sep 2009
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    Observe your sum is bounded above by the integral of 1 \x^k from M to N-1, which you can easily evaluate directly obtaining two terms bounded by C/M^(k-1) as needed.
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