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Math Help - Sequence limit problem

  1. #1
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    Sequence limit problem

    I have to show that if

    a_0+a_1+a_2+...+a_p=0 then \lim_{n\rightarrow\infty} (a_0\sqrt{n}+a_1\sqrt{n+1}+a_2\sqrt{n+2}+...+a_p \sqrt{n+p})=0

    Any ideas?


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  2. #2
    Super Member girdav's Avatar
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    Re: Sequence limit problem

    a_p=-\sum_{k=0}^{p-1}a_k so \sum_{k=0}^pa_k\sqrt{n+k}=\sum_{k=0}^{p-1}a_k\frac{k-p}{\sqrt{n+k}+\sqrt{n+p}}.
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