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Sum to Integral

  1. May 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that each limit is a definite integral.
    [tex]Lim (n \rightarrow \infty) [/tex] of [tex]\sum \frac{n}{n^{2}+i^{2}} [/tex] from [tex]i=1[/tex] to [tex]n[/tex]

    2. Relevant equations
    [tex]Lim (n \rightarrow \infty) [/tex] of [tex]\sum f(c)\Delta X [/tex] from [tex]i=1[/tex] to [tex]n[/tex]


    3. The attempt at a solution

    I can't really get this started, so any help at all would be great.

    Thanks.
     
  2. jcsd
  3. May 11, 2008 #2
    Try multiplying by [tex]\frac{\frac{1}{n^2}}{\frac{1}{n^2}}[/tex].
     
  4. May 11, 2008 #3

    HallsofIvy

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    Science Advisor

    What do you think [itex]\Delta x[/itex] should be?

    (My hint is really the same as foxjwill's.)
     
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