# Need to find a convergent value

1. Oct 15, 2005

### Werg22

Given this sum

$$s = \sum_{k = 1}^{{\frac{x}{j}} - 1} k^{n}j^{n+1}$$

x and n are constants

and x/j is a positive integrer and k is an integrer

To what value s converges as

$${j}{\rightarrow}{0}$$
?

Edit: I have found that the awnser is $$\frac{x^{n+1}}{n+1}$$, but i do not know how to obtain this...

Last edited: Oct 15, 2005
2. Oct 16, 2005

### Timbuqtu

What do you recognize if I write
$$s = \sum_{k=1}^{N-1} x_k^n \Delta x$$
where $$N = x/(\Delta x)$$ and $$x_k = k \Delta x$$? What about a Riemann sum?