# Proof of a Sum_Integral

1. Jun 23, 2010

### heinerL

Can anybody help me with the following:

[tex]\lim_{n \rightarrow \infty} = \frac{1^k+2+k+...+n^k}{n^{k+1}}=\frac{1}{k+1}[\tex]

How do you proof this equation with the Riemann-integral, especially with upper/lower riemann sums?

thank you!

2. Jun 23, 2010

### Staff: Mentor

Just some help with your LaTeX...

3. Jun 23, 2010

### g_edgar

Find a particular integral so that the fraction on the left-hand-side is the Riemann sum when the interval is divided into n equal parts. Then that limit is the value of the integral.