How to Prove a Sum_Integral Equation Using the Riemann-Integral?

[heinerL]

Can anybody help me with the following:

$$\lim_{n \rightarrow \infty} = \frac{1^k+2+k+...+n^k}{n^{k+1}}=\frac{1}{k+1}[\tex]<br /> <br /> How do you proof this equation with the Riemann-integral, especially with upper/lower riemann sums?<br /> <br /> thank you!$$

 

[Mark44]

Just some help with your LaTeX...

Can anybody help me with the following:

$$\lim_{n \rightarrow \infty} \frac{1^k+2^k+...+n^k}{n^{k+1}}=\frac{1}{k+1}$$

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

thank you!

 

[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.