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Thread: Big O

  1. #1
    Junior Member
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    Dec 2008
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    Big O

    Let $\displaystyle N > M $. Prove that for $\displaystyle k > 1 $, $\displaystyle \sum_{n=M+1}^{N} n^{-k} = O(M^{-k+1}) $ as $\displaystyle 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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