given that we have 2 series a_n and b_n that converges, does that mean that the product of this two series a_n b_n also converges?
what i said was that since both converge, the seq of finite partial sums for both will be bounded and hence
using cauchy seq,
sum from k = n to m of a_n b_n is also bounded.
since the product is cauchy, it is convergent.
is my reasoning right?