Fourier series

[foo9008]

Homework Statement

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 )

Homework Equations

The Attempt at a Solution

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[vela]

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.

 

[foo9008]

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

 

[Samy_A]

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

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?

 

[foo9008]

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?

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

 

[Samy_A]

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

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).

 

[foo9008]

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).

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

 

[Samy_A]

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

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.