(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].

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# Sum of a finite exponential series

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