# Thread: Convergence problem

1. ## Convergence problem

Determine whether the series converges absolutely, converges conditionally or diverges:

(The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1))

This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0.

Can anyone help me out here?

2. Anyone know what to do here?
I'm trying the integral test, but I'm not sure how to integrate:

1
-------
k^3 - 1

3. Originally Posted by TripleHelix
Determine whether the series converges absolutely, converges conditionally or diverges:

(The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1))

This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0.

Can anyone help me out here?
First compare the series $\displaystyle \sum_{k = 2}^{\infty} \frac{1}{k^3-1}$ with $\displaystyle \sum_{k = 2}^{\infty} \frac{1}{k^3}$ (limit comparison test) to check for absolute convergence.