Question

Explaination for why the radius of convergence of hte power series starting at n=0 to infirty of the function nFactorial(x-4)^n is 0

Answer 1

\[\sum_{n=0}^{\infty} n!(x-4)^n\]

Answer 2

use ratio test to see convergence at x=4:
\(n!(x-4)^n/(n+1)!(x-4)^{n+1}=1/(n+1)(x-4)<1\)
this is not happening fr any x . So radius=0