Hello, I need to check my answer:
The problem asks me to find the radius of convergence for:
inf
Sum
n=1
(-1)^n * x^(2n+1)
_________________
(2n+1)!
I preform the ratio test, use bn+1/bn...replace alln with n+1...times by reciprocal, etc...the typical method and get:
1/2|x^2/(n+1)(2n+3)|
Taking the limit, the answer = 0....thus the radius is then INFINTE.
So the radius is Infinity. If we were asked, then the int of convergence is (-inf, inf).
Is my answer right?
Yes, What is the radius of convergence. I do not need to state the interval but I thought as listed in my reasoning (that the interval was -inf to inf).
Can you show how you got a finite answer?
As said, I used ration test. Then replace all n with n+1. Set up bn+1/bn
If I work this out then I find the infinite solution for the radius. I then thought that the interval was not finite based upon the radius. Is the radius also not finite?