Absolute Convergence Proof: The Relationship Between a_k and b_k

[DEMJ]

Homework Statement

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

Homework Equations

It's either true or false.

The Attempt at a Solution

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

 

[lanedance]

that looks reasonable, if the ak & bk were positive numbers or it was written for maginutudes it would be true