intervals of convergence

Question

I am trying to find the interval of convergence for the power series: 2+4x^2+8x^4+16x^6...(2^n)x^(2(n-1))

What is the best way to do this? I can use the ratio test correct?  Are there any other ways of solving this? Please help with a good explaination. I really have no idea how to do this. Thanks.

Answer 1

1) Use the ration test  (You have to use it, no way around it)

2) Find the interval

3) Use the various tests(nth term test, etc) to figure out if you need to include the endpoints