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Sum to Integral

  • Thread starter dtl42
  • Start date
  • #1
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Homework Statement


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]

Homework Equations


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


The Attempt at a Solution



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

Thanks.
 

Answers and Replies

  • #2
354
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Try multiplying by [tex]\frac{\frac{1}{n^2}}{\frac{1}{n^2}}[/tex].
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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What do you think [itex]\Delta x[/itex] should be?

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

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