Problem 1112 (difficulty: 2/10)

Prove that if \(\displaystyle \sum a_n\) and \(\displaystyle \sum b_n\) are absolutely convergent, then the following series are also absolutely convergent:

\(\displaystyle \sum(a_n+b_n) \qquad \sum\max(a_n, b_n) \qquad \sum\sqrt{a_n^2+b_n^2} \)

Give me another random problem!