How to Convert Fourier Series to Exponential Form?

[Leumas13]

So, I've been asked to show that
f(x)=Ʃ_n=0^∞ [a_nsin(nπx/a) + b_ncos(nπx/a)

is equivalent to f(x)=Ʃ_n=-∞^∞ c<sub>ne^inx/a



I'm kinda stuck. i want to turn this into the exponential form but I don't see how to condense this into a single term.



Thanks!</sub>

 

[Leumas13]

Nevermind, Solved

Use the substitution that sinu = 0.5i (e^iu -e^-iu) and the equivalent for cosine and shift the register of the summation.