Examine the continuity of $f(x)=x^2+\frac{x^2}{(1+x^2)}+\frac{x^2}{(1+x^2)^2}+...+ \frac{x^2}{(1+x^2)^n}+....$ at $x=0$ 
Examine the continuity of $$f(x)=x^2+\frac{x^2}{(1+x^2)}+\frac{x^2}{(1+x^2)^2}+...+ \frac{x^2}{(1+x^2)^n}+....$$ at $x=0$

I tried to solve the problem using $$\lim_{x \to0^+}f(x)=\lim_{x \to0^-}f(x)=f(0)$$ and I got both limits to be $0$. I think there is an error somewhere since my book says it is discontinuous.
Can you help me out?
 Thankyou

Note that it's a geometric series, as Haral Hanche-Olsen commented. You can write $f(x)$ as
$$f(x) = x^2 \frac{1-\frac{1}{(1+x^2)^{n+1}}}{1-\frac{1}{1+x^2}}=x^2\frac{(1+x^2)^{n+1}-1}{x^2(1+x^2)^{n}} = \frac{(1+x^2)^{n+1}-1}{(1+x^2)^{n}}$$
This function is continuous at $x=0$ in my sense...
