Question: Consider the series $g_n(x)=\sum_{k=0}^n\cfrac{x^2}{(1+x^2)^k}$ Prove that the series converges pointwise to the function $$g(x)=\begin{cases} 0 & \text{ if } x=0 \\ 1+x^2 & \text{ if } x \neq 0 \end{cases}$$ but the convergence is not uniform on any interval containing $0$ on its interior.
Help? Not even sure what the first step is on this one.