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

[skyturnred]

Homework Statement

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}

Homework Equations

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!

 

[micromass]

Maybe write

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

 

[skyturnred]

Maybe write

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

Thanks! I got it! Your response in combination with all the help you gave me yesterday definitely helped me understand Rieman sums!