Converting a Sum to a Riemann Sum and Finding its Limit

[Sean1218]

Homework Statement

Find lim_n->∞ (1/n)(Ʃ_{k=1 to n} ln(2n/(n+k)))

Homework Equations

The Attempt at a Solution

I'm not sure if this is even a riemann sum at all, but I don't see what else it could be. I wanted to find the riemann portion first to get rid of the sigma notation then find the limit of everything, but I don't have any of the information I need to do the riemann sum or to convert it to an integral.

 

[Sean1218]

I realize I need to be able to put it in a form of (b-a)/n Ʃ (a+(b-a)k/n), but I'm not sure how I can work with ln and manipulate it when everything is stuck in ln. Any tips?

 

[Dick]

If you can put it in the form of sum (1/n)f(k/n) for some function f then it's a Riemann sum of the function f(x) for x=0 to 1. What's f?