true or false:

Question

if the sum from n=1 to infinity of a(n) converges, and the sum from n=1 to infinity of b(n) diverges, then the series from n=1 to infinity of (a(n)*b(n)) diverges

i said this was true... is this correct?

Answer 1

I don't know.
What if
An = 1/x^5
and Bn = x^2
then An*Bn = 1/x^3