Thread: Series of Functions

Hi,

I would like to know how to prove the following:

Prove that
Summation of n from (0 to infinity): (e^-nx)(Sin nx)
converges to a continuous function on (0,infinity)

So, I will have to show it is uniform on [a,infinity) for every a > 0 and then what should I do next?

Can someone please help me on this? Thank you!

Since it is clear that all of these functions are continuous for all n, showing that convergence is uniform is all you need!