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

[nomadreid]

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 |a_n/a_n+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?

 

[pwsnafu]

What am I doing wrong?

We can't answer that unless you write your calculations.

 

[nomadreid]

Thanks for replying: I don't usually do that: send in the mail without checking first and of course without putting down my calculations, but I was about to head off to commute to give my course and noticed the anomaly, so I shot off the mail, but found the error while waiting for the bus. My apologies for the panic.