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

[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]

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->∞ [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!

 

[micromass]

Maybe write

[tex]\frac{1}{n+i}=\frac{1}{n}\frac{1}{1+\frac{i}{n}}[/tex]

 

[skyturnred]

Maybe write

[tex]\frac{1}{n+i}=\frac{1}{n}\frac{1}{1+\frac{i}{n}}[/tex]

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