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Math Help - Series Help(Limit And Submation)

  1. #1
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    Series Help(Limit And Submation)

    <br />
\lim_{n\to\infty} \sum^{n}_{k=1} \frac{1}{\sqrt{k}(k+3)+k\sqrt{k+3}}<br />
    please tell me the calculating and Thankyou!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by frercss View Post
    <br />
\lim_{n\to\infty} \sum^{n}_{k=1} \frac{1}{\sqrt{k}(k+3)+k\sqrt{k+3}}<br />
    Multiplying \frac{1}{\sqrt{k}(k+3)+k\sqrt{k+3}} by \frac{\sqrt{k}(k+3)-k\sqrt{k+3}}{\sqrt{k}(k+3)-k\sqrt{k+3}}=1 I get that \frac{1}{\sqrt{k}(k+3)+k\sqrt{k+3}}=\frac{1}{3\sqr  t{k}}-\frac{1}{3\sqrt{k+3}}. If you sum these terms for k such that 1\leq k\leq n you'll see that many of them "disappear".
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