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