Help me find the radius of convergence?

[madcattle]

Homework Statement

Ʃn!(x-1)ⁿ
I need to find the radius of convergence for this summation from n=0 to n=∞

The Attempt at a Solution

I started off with the ratio test:

(n!(n+1)(x-1)(x-1)ⁿ)/(n!(x-1)ⁿ) = (n+1)(x-1)

(x-1)lim(n+1)...Now at this point it looks to me like the series does not actually converge, but my book is telling me that it does. Am I looking at something the wrong way? Not actually understanding the problem?

 

[ross1219]

It looks like it converges only at x = 1.

 

[Bohrok]

Usually you do the ratio test on the part of the sum that doesn't have the factor with x, so in this case with just n!. Simplifying that gets you L = lim_n→∞(n+1) = ∞ and the radius of convergence is r = 1/L = 0.

The only x value where it converges is x=1.