What Definite Integral Does This Riemann Sum Represent?

[aselin0331]

Homework Statement

Rn=\sum(i*e^(-2i/n))/n^2, i=1

Identify this Riemann sum corresponding to a certain definite integral.

Homework Equations

The Attempt at a Solution

I got till 1/n^2 [1/e^(2/n)+2/e^(4/n)+3/e^(6/n)...n/e^2]

and that's it. To my understanding I should be able to pull something else out of the square brackets but I tried so long with no success.

Help?

 

[Office_Shredder]

Actually, you want to put something back into the square bracket.

Your function f(x) is going to turn into summing up values of the function that looks like f((b-a)i/n) because you break up the interval into n pieces and sum over the value on each piece. So your objective is to pair up i's and n's