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Math Help - Limit Problem

  1. #1
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    Limit Problem

    Hi everyone.
    I've tried to solve this limit; but I really don't know how to treat it.
    \displaystyle \lim_{n \rightarrow\infty} \sum_{i=1}^n \frac{n}{n^2 + i^2}
    I appreciate your help.
    everk.
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by everk View Post
    Hi everyone.
    I've tried to solve this limit; but I really don't know how to treat it.
    \displaystyle \lim_{n \rightarrow\infty} \sum_{i=1}^n \frac{n}{n^2 + i^2}
    I appreciate your help.
    everk.
    Are you studying the Riemann integral by any chance? Divide top and bottom of that sum by n^2 so that it becomes \displaystyle\frac1n \sum_{i=1}^n \frac{1}{1 + (i/n)^2} , and think of that as a Riemann sum for an integral.
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