# Math Help - A proof of convergence of an infinite series

1. ## A proof of convergence of an infinite series

Show that if $\sum$ a_k is absolutely convergent and abs(b_k) $\leq$ abs(a_k) fopr all k, then $\sum$ b_k is absolutely convergent

Here is what I have for this:
Because abs(b_k) $\leq$ abs(a_k), then $\sum$ abs(b_k) $\leq$ $\sum$ abs(a_k)
With the basic comparison test, since $\sum$ abs(a_k) is convergent, then $\sum$ abs(b_k) is convergent
Since $\sum$ abs(b_k) is convergent, by theorem $\sum$ bk converges and is absolutely convergent.

Is this proof sufficient?

2. Yes that is a proof.
You may want to add that ${\color{blue}{0 \leqslant}} \sum {\left| {b_n } \right|}$, just to be complete.