Question

Determine if the following statements are true or false

A) If Σ|an + bn| converges, then Σ|an| converges and Σ|bn|converges.

B) If the terms, a_n, of a series approach zero as n approaches infinity, then the series Σa_n converges.

Answer 1

A counter-example for B: consider the series \(\displaystyle \sum_{n=1}^\infty\frac{1}{n}.\) This is a divergent series, despite the fact that \(\displaystyle\lim_{n\to\infty}\frac{1}{n}=0\).

Answer 2

what about A?

Answer 3

Still thinking about it...