# Thread: Evaluating endpoints for conditionally or absolute convergence

1. ## Evaluating endpoints for conditionally or absolute convergence

Q1)
(x^n) / ((2^n)*ln(n)) = x is on the interval of -2 to 2. All of this is correct so far, however, I trouble evaluating the endpoints to see if they conditionally/absolute converges or diverges. According to the book answer, -2 conditionally converges, which I dont quite understand.

My question is, how do I evaluate the endpoints for convergence/divergence? I plugged the numbers in, but dont quite grasp how to proceed from there.

2. If $S(x) = \sum\limits_n {\frac{{x^n }}{{2^n \ln (n)}}}$ then $S(2) = \sum\limits_n {\frac{1}{{\ln (n)}}}$ clearly diverges.

Whereas, $S( - 2) = \sum\limits_n {\frac{{\left( { - 1} \right)^n }}{{\ln (n)}}}$ converges by the alternating series test.

Does this help?

3. Thank you! I understand it now.