Let $\displaystyle \sum_{n=0}^{\infty} a_n $ and $\displaystyle \sum_{n=0}^{\infty} b_n $ be absolutely convergent (complex) series with sums A and B respectively. For each n, define $\displaystyle c_n = \sum_{m=0}^{n} a_m b_{n-m}$.

1. Show that $\displaystyle \sum_{n=0}^{\infty} c_n $ is absolutely convergent. [Hint: Follow the same basic plan as used in Prop 5.2 (a) ]

Now the proposition says : Suppose $\displaystyle \sum_{n=0}^{\infty} a_n $ is an absolutely convergent series (in $\displaystyle \mathbb{C} $ ) which has sum S. Then any rearrangement is also absolutely convergent and has sum S.

I am stumped I don't even have a beginning of an idea what to do

. There are even parts after this question too which make even less sense to me but I think tackling this bit is the first step. any help would be appreciated