Homework Help: Determine if series converges

1. May 17, 2010

ziggie125

1. The problem statement, all variables and given/known data

Is the series convergent

1) $$\sum$$1/(n^2 * ln n)

and 2) which value of p does the series converge. $$\sum$$ 1/(n*(ln n)^p)

3. The attempt at a solution

1)

I cannot see how the root method ($$\sqrt[n]{Cn}$$) would work, or the ratio test would work (cn+1)/cn

Unless you use the limit test and lim 1/(n^2 * ln n) = 1/infinity = 0 therefore the series converges. I didnt think that question would be that easy though.

2) Similiar to the first wouldn't it just be if P > 1.

2. May 17, 2010

Staff: Mentor

The test you are thinking of, I believe, is the nth term test for divergence. If lim an != 0, the series diverges. You cannot use this test to conclude a series converges.

A test that might be useful in this problem is the comparison test.