Homework SourseI was asked to find the radius of convergence of k5 xk k0 va
I was asked to find the radius of convergence of k!/5 (x^k), (k=0, values go to infinity).
So, I started out by using the ratio test which got me lim k -> infinity = (k+1)! / k! which does not seem reasonably correct at all. Id appreciate any help, thank you very much in advance :)
So, I started out by using the ratio test which got me lim k -> infinity = (k+1)! / k! which does not seem reasonably correct at all. Id appreciate any help, thank you very much in advance :)
Solution
Tk - kth term : | Tk+1/Tk | : | (k+1)/x | < 1 radius of convergence is when you remove the variable part and just consider the ramaining terms |k+1| < 1 radius = 1/(k+1) where k tends to infinity radius = 0 but when it comes to find value of variable x then interval of convergence comes in |1/x| <= 0 x = ( - infinty , infintiy ) answer !!!
