Conditionally convergence of a product of a conditonally convergent series

[jonsteadinho]

Homework Statement

1. Find a function such that infinite sum of a_nis conditionally convergent but infinite sum of (a_n)^3 does not converge conditionally

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.

Homework Statement

 

[lippyka]

2. Find the value of the sumS=1+2+3+4+....+2015The Attempt at a SolutionWe can use the formula for the sum of an arithmetic sequence:S=n/2(a1+an)Where n is the number of terms and a1 and an are the first and last terms.In this case, n=2015, a1=1, an=2015Therefore, S= 2015/2(1+2015)=1512060