Solution
= Solution
If $|f_n(x)|\le M_n$ and $\sum M_n\lt \infty$, then every tail is bounded uniformly by the corresponding numerical tail. The uniform Cauchy criterion therefore proves <uniform convergence>.
= Solution
If $|f_n(x)|\le M_n$ and $\sum M_n\lt \infty$, then every tail is bounded uniformly by the corresponding numerical tail. The uniform Cauchy criterion therefore proves <uniform convergence>.