- #1
lys04
- 113
- 4
- Homework Statement
- pointwise convergence of a series
- Relevant Equations
- $$ \sum_{n=1}^\infty sin(\frac{n\pi}{2})sin(nx) $$
How do I know whether or not the series
$$ \sum_{n=1}^\infty sin(\frac{n\pi}{2})sin(nx)$$
converges pointwise for all real x or not?
By the way am I right in thinking that converging pointwise for all real x means whatever x i plug into the series it converges to some finite value?
I was thinking if i plug in x=pi/2 then I'd get
$$ \sum_{n=1}^\infty sin^2(\frac{n\pi}{2}) $$
Which diverges, does that prove that the series doesn't converge pointwise for all x?
$$ \sum_{n=1}^\infty sin(\frac{n\pi}{2})sin(nx)$$
converges pointwise for all real x or not?
By the way am I right in thinking that converging pointwise for all real x means whatever x i plug into the series it converges to some finite value?
I was thinking if i plug in x=pi/2 then I'd get
$$ \sum_{n=1}^\infty sin^2(\frac{n\pi}{2}) $$
Which diverges, does that prove that the series doesn't converge pointwise for all x?