ratio test for sum [n=0, infty] [ n! (x - 4)^n ]

[cheffy]

I have this series:

\(\displaystyle \
\sum\limits_{n = 0}^\infty\, {n!\, (x\, -\, 4)^n }
\\)

I took the limit of this for the ratio test and I got:

\(\displaystyle \
\lim\limits_{n \to \infty }\, (n\, +\, 1)(x\, - \, 4)
\\)

Does that mean that this diverges except for x = 4? Or am I doing something wrong?

Thanks!

 

[pka]

Yes, that is correct.