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

True.

In order for the a subn series to converge, an infinite number of terms past some n value must be <0 , individually. That means there must be an infinite number of terms >0 in the 1/asubn series. Therefore it cannot converge.