Convergence of sine series

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PedroGzlez

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Find all real x values such that the series sin(nx)/(n+1) converges. I have been trying all day but nothing comes into mind. Without using Abel or Dirichlet criteria, please.
 
PedroGzlez said:
Find all real x values such that the series sin(nx)/(n+1) converges. I have been trying all day but nothing comes into mind. Without using Abel or Dirichlet criteria, please.
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Are you trying to refer to a SERIES of SEQUENCE ?
 
Prof. Khan is asking you, do you mean this?

\(\displaystyle \sum_{n=0}^{\infty} \frac{\sin(nx)}{n + 1}\)
 
PedroGzlez said:
Find all real x values such that the series sin(nx)/(n+1) converges. I have been trying all day but nothing comes into mind. Without using Abel or Dirichlet criteria, please.
Click to expand...
Did this come from a Fourier Series? Is it a problem you know the answer from the Dirichlet conditions on a Fourier Series and you are trying to prove convergence directly from the series?
 
LCKurtz said:
Did this come from a Fourier Series? Is it a problem you know the answer from the Dirichlet conditions on a Fourier Series and you are trying to prove convergence directly from the series?
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Welcome back LC !!!!
 
PedroGzlez said:
Find all real x values such that the series sin(nx)/(n+1) converges. I have been trying all day but nothing comes into mind. Without using Abel or Dirichlet criteria, please.
Click to expand...
[imath]\sin(x)=\displaystyle{\sum\limits_{k = 0}^\infty {\frac{{{{\left( { - 1} \right)}^k}{x^{2k + 1}}}}{{\left( {1 + 2k} \right)!}}}}[/imath] the sine series converges [imath]\forall x\in\Re[/imath].
Do you see from this, why [imath]\sin(x)[/imath] is an odd function?

[imath][/imath][imath][/imath][imath][/imath][imath][/imath]
 
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