# Thread: Clarification of Alternating Series test

1. ## Clarification of Alternating Series test

I need to determine whether $\sum_{n=2}^\infty (-1)^n \frac {x^n}{4^n ln(n)}$ diverges at x= -4, and x=4.

I want to use the alternating series test, but my book defines it as starting at n=1, not n=2 like in my problem.

Can I use the test as it is? Do I need to manipulate it? If I need to manipulate it, would this be a valid manipulation?:
$= \sum_{n=1}^\infty (-1)^{n+1} \frac {x^{n+1}}{4^{n+1} ln(n+1)} = \sum_{n=1}^\infty (-1)^{n-1} \frac {x^{n+1}}{4^{n+1} ln(n+1)}$

I'm fairly certian it is, but I'm still a tad bit shaky with these.

2. Hello,

Adding or removing a finite number of terms is not important when it's about to talk about convergence and divergence... I think... This has to deal with Cauchy's criteria. But it has been months since i have done this.

Otherwise, yeah, a variable change can fit in

3. Originally Posted by Moo
Adding or removing a finite number of terms is not important when it's about to talk about convergence and divergence... I think...
It is okay