# Series and convergence/divergence

1. Feb 29, 2008

### Niles

1. The problem statement, all variables and given/known data
Determine whether the series converges:

$$\sum\limits_{n = 2}^{\inf } {\frac{{( - 1)^n (n^2 + 1)^{1/2} }}{{n\ln (n)}}}$$

3. The attempt at a solution

Which test must I use? I thought of using the integral test, but it seems a little too hard. Are there other possibilities?

2. Feb 29, 2008

### foxjwill

Try either the ratio or root test. Neither would be very easy to calculate, but...

3. Feb 29, 2008

### NateTG

Well, the $(-1)^n$ should give you an easy test...

BTW: \infty is $\infty$

4. Feb 29, 2008

### Niles

Should I just take:

$$\sum\limits_{n = 2}^{\inf } {\frac{{( - 1)^n (n^2 + 1)^{1/2} }}{{n\ln (n)}}}^{(1/n)}$$ and take the limit of this?

5. Feb 29, 2008

### chaoseverlasting

Its an alternating series, what about the Leibinitz test?

6. Mar 1, 2008

### Niles

I looked at the Leinitz test - on wikipedia they write about the first condition:

"If the sequence a_n converges to 0, and .." - does this mean the limit of a_n for n -> infinity?

Last edited: Mar 1, 2008