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Homework Help: Need helping evaluating this limit by expressing it as a definite integral

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data

    Evaluate the limit by expressing it as a definite [STRIKE]interval[/STRIKE] integral

    [itex]\frac{lim}{n \rightarrow \infty}[/itex] ([itex]\frac{1}{n+1}[/itex]+[itex]\frac{1}{n+2}[/itex]+...+[itex]\frac{1}{n+(n-1)}[/itex]+[itex]\frac{1}{n+n}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    OK, so I know it has to do with Rieman sums. So I know I have to express it as

    lim n->∞ [itex]\sum[/itex][itex]^{n}[/itex][itex]_{i=1}[/itex]f(x[itex]_{i*}[/itex])Δx

    So I was able to change the original question into the following form:

    lim n->∞ [itex]\sum[/itex][itex]^{n}[/itex][itex]_{i=1}[/itex][itex]\frac{1}{n+i}[/itex]

    But I cannot find something that I can take out of that as Δx, nor can I find a way to find a or b to plug into the formula Δx=[itex]\frac{b-a}{n}[/itex]. Also, for the same reason, I cannot find f(x[itex]_{i}[/itex]*) or x[itex]_{i}[/itex]*. Can anyone help? Thanks!
     
    Last edited by a moderator: Dec 1, 2011
  2. jcsd
  3. Dec 1, 2011 #2
    Maybe write

    [tex]\frac{1}{n+i}=\frac{1}{n}\frac{1}{1+\frac{i}{n}}[/tex]
     
  4. Dec 1, 2011 #3
    Thanks! I got it! Your response in combination with all the help you gave me yesterday definitely helped me understand Rieman sums!
     
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