# Conditionally convergence of a product of a conditonally convergent series

1. Apr 12, 2009

1. The problem statement, all variables and given/known data
1. Find a function such that infinite sum of anis conditionally convergent but infinite sum of (an)^3 does not converge conditionally

3. The attempt at a solution
We have confusions about the definition of conditional convergence. Importantly, does absolute convergence also mean conditional convergence? If not, then the sum a simple function an= (-1)n*1/n is conditionally convergent but the sum of its cube is absolutely convergent

However, if absolute means conditional, then we need to find an such that (an)^3 diverges under all conditions.
1. The problem statement, all variables and given/known data