Fourier series

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  • #1
678
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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 )
2CYgve2.jpg


xH4yExE.jpg

Homework Equations




The Attempt at a Solution


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Answers and Replies

  • #2
vela
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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.
 
  • #3
678
4
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....
 
  • #4
Samy_A
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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?
 
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  • #5
678
4
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??
 
  • #6
Samy_A
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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).
 
  • #7
678
4
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)
 
  • #8
Samy_A
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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.
 

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