Conditionally convergence of a product of a conditonally convergent series

jonsteadinho

1. The problem statement, all variables and given/known data
1. Find a function such that infinite sum of a_nis conditionally convergent but infinite sum of (a_n)^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 a_n= (-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 a_n such that (a_n)^3 diverges under all conditions.
1. The problem statement, all variables and given/known data