# Math Help - How to write this function as an integral?

1. ## How to write this function as an integral?

Prove that the following sequence converges, and find its limit.

$a_n=\frac{1}{n^3}\sum_{k=1}^nk^2cos(\frac{k\pi}{n} )$

I'm stuck on just determining what function this is...
I know $b-a=1$ and (I think) $a=0$ so the integral is from 0 to 1. Any other help on this?

2. It's a Riemann sum for the function $f(t)=t^2\cos(\pi t),$ can you see why?

3. Originally Posted by Krizalid
It's a Riemann sum for the function $f(t)=t^2\cos(\pi t),$ can you see why?
That's what I thought, I just wasn't sure. The sum is from 0 to 1, right?

4. Yes.