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Math Help - Riemann Sums

  1. #1
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    Riemann Sums

    Show that \lim_{n\rightarrow\infty}\sum_{i=0}^n\frac{1}{n+i}  =\log 2 by writing the sum under the limit as the Riemann sum of an appropriate function.
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Show that \lim_{n\rightarrow\infty}\sum_{i=0}^n\frac{1}{n+i}  =\log 2 by writing the sum under the limit as the Riemann sum of an appropriate function.

    \lim_{n\rightarrow\infty}\sum_{i=0}^n\frac{1}{n+i}  =\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=0}^n\  frac{n}{n+i}= \lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=0}^n\f  rac{1}{1+i/n}=:\int\limits^2_1\frac{dx}{x}

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