Originally Posted by

**magus** That's my problem I was using $\displaystyle \sum_{k = 1}^{n} r^{k} = \frac{1 - r^{n+1}}{1 - r}$ and never thought of futtzing with that.

So for $\displaystyle a=e^{i\theta}$, $\displaystyle r=e^{i2\theta}$, and we obviously get $\displaystyle \displaystyle \frac{e^{i \theta} (1 - (e^{i2\theta})^n)}{1 - e^{i\theta}}$

Now what I don't see is how you get$\displaystyle \displaystyle \frac{e^{i \theta} (1 - (e^{i2\theta})^n)}{1 - e^{i\theta}} = \frac{1 - e^{i2n\theta}}{e^{-i\theta} - e^{i\theta}}$ because for me if I bring the $\displaystyle e^{-i\theta}$ into the denominator I get

$\displaystyle \displaystyle \frac{ (1 - (e^{i2\theta})^n)}{e^{-i \theta}(1 - e^{i\theta)}}=\frac{1 - e^{i2n\theta}}{e^{-i\theta} - e^{-i\theta}e^{i\theta}}=\frac{1 - e^{i2n\theta}}{e^{-i\theta} - 1}$