Evaluating an Infinite Series (non geometric)

[randomguyruch]

Homework Statement

http://bit.ly/9N9iLZ

Evaluate:
lim n-> infinity of Sum (from k = 1 to n) of sqrt(k/n) * 1/n

Homework Equations

taylor series?

The Attempt at a Solution

the above = lim n->infinity of Sum (from k = 1 to n) of k^1/2 / n^3/2
k approaches n so
n^1/2 / n^3/2 -> 1/n -> diverge

correct answer is 2/3 i have no idae how to get it help

 

[willem2]

Your sum is the approximation of an integral of a certain function from 0 to 1 with n values. If n->inf then the limit of the approximation becomes is the integral.