(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

if [itex]a_k \le b_k[/itex] for all [itex]k \in \mathbb{N}[/itex] and [itex]\sum_{k=1}^{\infty} b_k[/itex] is absolutely convergent, then [itex]\sum_{k=1}^{\infty} a_k[/itex] converges.

2. Relevant equations

It's either true or false.

3. The attempt at a solution

I think a counterexample to prove it's false is if we let [itex]a_k=-1, b_k = 0[/itex] which satisfies [itex]a_k \le b_k[/itex] and [itex]b_k[/itex] is abs. convergent but [itex]\sum_{k=1}^{\infty} a_k[/itex] diverges.

Is this a correct counterexample?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Abs. Convergence Proof

**Physics Forums | Science Articles, Homework Help, Discussion**