(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given is [itex]\sum_{n=-N}^{N}e^{-j \omega n} = e^{-j\omega N} \frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}[/itex]. I do not see how you can rewrite it like that.

2. Relevant equations

Sum of a finite geometric series: [itex]\sum_{n=0}^{N}r^n=\frac{1-r^{N+1}}{1-r}[/itex]

3. The attempt at a solution

Or is the above result based on this more general equation: [itex]\sum_{n=0}^{N}ar^n=a\frac{1-r^{N+1}}{1-r}[/itex]? Although I think the equation in (2) is just this equation for a=1, right?

So, I know how to get to the 2nd term in (1), i.e., [itex]\frac{1-e^{-j \omega (2N+1)}}{1 - e^{-j\omega}}[/itex], but I have no idea why it is multiplied by the term [itex]e^{-j\omega N}[/itex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sum of a finite exponential series

**Physics Forums | Science Articles, Homework Help, Discussion**