What is the convergence of a power series using the ratio test?

[rcmango]

Homework Statement

I've tried to apply the ratio test to a problem that is a power series. here's the problem as a pic: http://img152.imageshack.us/img152/2751/35685690oj3.png

Homework Equations

The Attempt at a Solution

I've gotten so far as you can see in the pic, I've skipped all my work, but if someone can go through the problem, you'll see where I'm stuck, I'm not sure what to do with the n/(n+1) ...just use nth term test.. to get 1?

then also, |x+2|/2 ... I'm unsure if it just stays that way?

and the big problem is my (-1)^n i can't divide that through the numerator because of the n right?

there is my effort, now please just help me to achieve the end, i don't have much time.

i know the answer is 2, (4, 0]

 

[danni7070]

$$\frac{n}{n+1}*\frac{2^n}{2^{n+1}}*\frac{(x+2)^{n+1}}{(x+2)^n}$$

I get this if I just skip the (-1)^n part cos you just know it is 1, -1, 1, -1 for different values of n which tells you that the sum is alternating.