How to Prove This Fourier Series Summation Equation?

[thelegend09]

Fourier series summation...help!

Basically, i need to show that...

2 + sum (m=1 to n) [4(-1)^m . cos(m.pi.x)] = 2(-1)^n.cos((n+1/2)pi.x)/cos((pi.x)/2)

Any ideas?

 

[Andrew Mason]

Basically, i need to show that...

$$2 + \sum_{m=1}^n 4(-1)^m\cos{(m\pi x)} = 2(-1)^n\cos((n+\frac{1}{2})\pi x)/\cos{(\pi x/2})$$

Try writing the right side function as a Fourier series.

AM