Math Help - how to show this series uni. convergent

1. how to show this series uni. convergent

2. Originally Posted by silversand
Since $|u_n(x)|\leq M_n$, then for large enough $n,m$, we can say that $\left|\sum_{i=n}^m u_i(x)\right|\leq\sum_{i=n}^m M_i < \epsilon$ for all $x$.

Letting $m\to\infty$, we can say that $\exists~N$ such that $n>N \implies |u_n(x)-u(x)|<\epsilon$, so $u_i$ converges uniformly to $u$.

3. Weierstrass M-test.