# Fourier series

1. May 8, 2016

### foo9008

1. The problem statement, all variables and given/known data
the answer that i get is different with the answer provided , is my answer wrong ? i got ( cos(2n -1) / 2n-1 )instead of ( cos(n+1) / n+1 )

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 8, 2016
2. May 8, 2016

### vela

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

3. May 9, 2016

### foo9008

I am not interested in the graph, I just wanna know the final answer....

4. May 9, 2016

### Samy_A

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?

Last edited: May 9, 2016
5. May 9, 2016

### foo9008

Cos(n +1 ) pi= (-1)^n.... What can we conclude from that??

6. May 9, 2016

### Samy_A

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).

7. May 9, 2016

### foo9008

It's (-1) ^ (n +1)

8. May 9, 2016

### Samy_A

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.