Does the sequence of functions defined by $f_{n}(x)=(1+x^{2n})^{1/2n}$ converge uniformly on $\mathbb{R}$.
For testing uniform convergence i know if the sequence $x_{n} = \sup \: \{ |f_{n}(x)-f(x) | : x \in \mathbb{R}\}$ converges to $0$ then $f_{n} \to f$ uniformly. But I don't know how to actually apply this result.