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

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SUMMARY

The discussion centers on the radius of convergence for the Taylor series expansion of ln(x) around a=2. The user initially calculated an infinite radius of convergence using the formula lim as n approaches infinity of |an/an+1|, which led to confusion regarding its validity. Upon further reflection, the user identified an error in their calculations, clarifying that the infinite radius of convergence does not imply validity everywhere for the function ln(x).

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nomadreid
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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?
 
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nomadreid said:
What am I doing wrong?

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

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