I have not been able to completely solve this problem and it's driving me crazy. Could you please help.
The question is to show that, $\sum_{n=1}^N \frac{\sin n\theta}{2^n} =\frac{2^{N+1}\sin\theta+\sin N\theta-2\sin(N+1)\theta }{2^N(5-4\cos\theta)}$ Where do I start? I tried solving this using de Moivre's Theorem but I don't know where I am going wrong. Could you please help me or if possible show other ways to tackle this particular problem.
Any Help is much appreciated!
Thanks in Advance!