Let a $\displaystyle \in$ (0,1). Show that the functional series

$\displaystyle \displaystyle\sum_{j=0}^{\infty}(-t^2)^j$ where $\displaystyle t \in [-a,a]$

is uniformly convergent with the limit function

$\displaystyle f(t) = \frac{1}{1+t^2}$

I have absolutely no clue where to go from here.

Any help???