Proving a sum that contains complex numbers

[homad2000]

Homework Statement

show that:

I tried changing the form to the sin and cos, but I couldn't complete it..

Any hints?

 

[HallsofIvy]

That's a geometric sequence. The sum of any geometric series is
$$\sum_{n=0}^\infty r^n= \frac{1}{1- r}$$

Here, your r is $e^{id}/2$.

 

[homad2000]

aaaah!

thanks for the help!