Fourier series

It's easy enough to check yourself. Try plotting each series. You only need 4 or 5 terms each.

www.desmos.com is useful if you don't have access to plotting software.

 

I actually followed vela's good advice, and the result is telling ...

Another test you could try: what happens with the given solution (answer b) when x=π?

 

No, that is not correct.
##\cos 2 \pi = \cos (1+1) \pi \neq {(-1)}^1##

Once you have the correct values, plug them in into the Fourier series of answer (b).

 

Correct.

So what is the Fourier series of answer (b) for x=π? Does it converge? If so, to what value?

And don't forget about vela's advice: it takes 2 minutes, and yields very interesting information.