# Sum to Integral

1. May 10, 2008

### dtl42

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

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

3. The attempt at a solution

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

Thanks.

2. May 11, 2008

### foxjwill

Try multiplying by $$\frac{\frac{1}{n^2}}{\frac{1}{n^2}}$$.

3. May 11, 2008

### HallsofIvy

What do you think $\Delta x$ should be?

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