# Rewriting a symbolic Summation

1. Apr 1, 2014

2. Apr 1, 2014

### Staff: Mentor

Pick a value for N, and expand the summation.
Pick a different value for N, and expand the summation.
After you do this a few times, maybe you can discover a pattern.

3. Apr 1, 2014

### Ray Vickson

Standard method:
$$\sum_{n=a}^{b} \cos(nw) = \frac{1}{2}\sum_{n=a}^{b} \left(e^{inw} + e^{-inw} \right)$$
This is a sum of two geometric series $\sum r^n$ with $r = e^{iw}$ and $r = e^{-iw}$.