Prove or disprove absolute convergence Prove or Disprove:
if $\sum_{n=1}^{\infty} a_n$ is absolutely convergent, then $\sum_{n=1}^{\infty} max\{a_n,\frac{1}{n^2}\}$ is also absolutely convergent.

ok, I think I just missed something pretty simple:
The sum of two convergent series is also convergent.
$\sum_{n=1}^{\infty} max\{a_n,\frac{1}{n^2}\} < \sum_{n=1}^{\infty} |a_n| + \sum_{n=1}^{\infty} |\frac{1}{n^2}| $
therefore by the first comparison test, the original series is absolutely convergent.
