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

1. Dec 1, 2011

### skyturnred

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

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

$\frac{lim}{n \rightarrow \infty}$ ($\frac{1}{n+1}$+$\frac{1}{n+2}$+...+$\frac{1}{n+(n-1)}$+$\frac{1}{n+n}$

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->∞ $\sum$$^{n}$$_{i=1}$f(x$_{i*}$)Δx

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

lim n->∞ $\sum$$^{n}$$_{i=1}$$\frac{1}{n+i}$

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=$\frac{b-a}{n}$. Also, for the same reason, I cannot find f(x$_{i}$*) or x$_{i}$*. Can anyone help? Thanks!

Last edited by a moderator: Dec 1, 2011
2. Dec 1, 2011

### micromass

Maybe write

$$\frac{1}{n+i}=\frac{1}{n}\frac{1}{1+\frac{i}{n}}$$

3. Dec 1, 2011

### skyturnred

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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