Let

and

be absolutely convergent (complex) series with sums A and B respectively. For each n, define

.

1. Show that

is absolutely convergent. [Hint: Follow the same basic plan as used in Prop 5.2 (a) ]

Now the proposition says : Suppose

is an absolutely convergent series (in

) 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