# Thread: Evaluating series

1. ## Evaluating series

i need help evaluating this: $\displaystyle \sum_{n=0}^\infty \frac{1}{2}^n {e^{-jw(n+1)}}$ i know the answer is: $\displaystyle {e^{-jw}}\frac{1}{1 - \frac{1}{2}e^{-jw}}$ however, im not quite sure how to get to it. I can kind of see how I could evaluate it, but is there a more general way to solve these?

2. Originally Posted by p00ndawg
i need help evaluating this: $\displaystyle \sum_{n=0}^\infty \frac{1}{2}^n {e^{-jw(n+1)}}$ i know the answer is: $\displaystyle {e^{-jw}}\frac{1}{1 - \frac{1}{2}e^{-jw}}$ however, im not quite sure how to get to it. I can kind of see how I could evaluate it, but is there a more general way to solve these?
You can re-arrange it into $\displaystyle e^{-jw} \sum_{n=0}^\infty \left( \frac{e^{-jw}}{2}\right)^n$ and then use the formula for the sum of an infinite geometric series.

3. Originally Posted by mr fantastic
You can re-arrange it into $\displaystyle e^{-jw} \sum_{n=0}^\infty \left( \frac{e^{-jw}}{2}\right)^n$ and then use the formula for the sum of an infinite geometric series.
ahh i see it now. Thanks.