Let (left{f_{n}(x)ight}_{n=1}^{infty}) and (left{g_{n}(x)ight}_{n=1}^{infty}) be sequences of real valued functions that converge uniformly on (mathbb{R}) to the

Question:

Let $\left\{f_{n}(x)ight\}_{n=1}^{\infty}$ and $\left\{g_{n}(x)ight\}_{n=1}^{\infty}$ be sequences of real valued functions that converge uniformly on $\mathbb{R}$ to the real functions $f$ and $g$ as $n ightarrow \infty$, respectively. Prove that $f_{n}+g_{n} \xrightarrow{u} f+g$ on $\mathbb{R}$ as $n ightarrow \infty$.

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