true of false

Question

if the sum of asubn from n=1 to infinity converges, and if a is not equal to 0, the the sum of 1/(a sub n) as n goes from 1 to infinity diverges.

Answer 1

Same answer as the other question.
If An converges, then An goes to zero for large n
if An goes to zero for large n, then 1/An goes to infinity
therefore 1/An can not converge.