Since it is clear that all of these functions are continuous for all n, showing that convergence is uniform is all you need!
I would like to know how to prove the following:
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!