How can I prove the convergence of this series?

[MAV]

How can I prove the convergence of this series?
Thank you !

 

[topsquark]

You might start with writing out an expression that can be read more easily.

Is it
[math]\sum_{m = 1}^{ \infty } \dfrac{ sin(m) ~ sin( m^2 ) }{2m^2 + 1} (x - 1)^{2m}[/math]
That doesn't look right to me.

I would imaging you are looking for the "radius of convergence?"

-Dan

 

[MAV]

You might start with writing out an expression that can be read more easily.

Is it
[math]\sum_{m = 1}^{ \infty } \dfrac{ sin(m) ~ sin( m^2 ) }{2m^2 + 1} (x - 1)^{2m}[/math]
That doesn't look right to me.

I would imaging you are looking for the "radius of convergence?"

-Dan