How should I show the absolute convergence of ?
I can't think of a test to use for a log function
What do you mean by absolute convergence? Do you mean if converges? If so just replace by in the following, it still holds. First we must have the convergence of . If that is true, then by definition . So using the limit comparison test we have . Now letting it is clear that since is a null sequence (it covnerges to zero) that As and we are left with