Radius of convergence around a=2 for ln(x)

Gold Member
When I use the calculation from Wikipedia that says that the radius of convergence of a series is lim as n goes to infinity of |an/an+1|, I get for the Taylor series expansion of ln(x) around a=2 the answer of an infinite radius of convergence, which would mean that it would be valid everywhere, which would not make sense. What am I doing wrong?