Convergence of sine series

[PedroGzlez]

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.

 

[Deleted member 4993]

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.

Are you trying to refer to a SERIES of SEQUENCE ?

 

[PedroGzlez]

Yes.

 

[nasi112]

Prof. Khan is asking you, do you mean this?

$\displaystyle \sum_{n=0}^{\infty} \frac{\sin(nx)}{n + 1}$

 

[PedroGzlez]

Yeah

 

[Deleted member 4993]

Yeah

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[nasi112]

Yeah

Hint: Apply alternating series test.

 

[LCKurtz]

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.

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?

 

[Deleted member 4993]

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?

Welcome back LC !!!!

 

[pka]

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.

$\sin(x)=\displaystyle{\sum\limits_{k = 0}^\infty {\frac{{{{\left( { - 1} \right)}^k}{x^{2k + 1}}}}{{\left( {1 + 2k} \right)!}}}}$ the sine series converges $\forall x\in\Re$.
Do you see from this, why $\sin(x)$ is an odd function?

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