Let , . Prove that on (-1,1).

I know that I need to prove uniform convergence on (-1,1). so, Let and for all . I know that converges to 0 and that is always between (-1,1). So using the Dirichlet's test for uniform convergence i should be able to prove is uniformly convergent and therefor . Will this work? and how do i write a formal proof if it is?