Uniform convergence of: $f_n(x) = \frac{1}{(1+x^2)^n},\text{ with } x\in \mathbb{R}$ Does the function defined by: 
$f_n(x) = \frac{1}{(1+x^2)^n},\text{ with } x\in\mathbb{R}$  converge uniformly in $\mathbb{R}$ ?

Every nonzero point must converge to $0$, but for any $n$, a sufficiently small positive $x$ satisfies $f_n(x) > \frac{1}{2}$. So the function does not uniformly converge.
