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

In summary, the conversation discusses the calculation for the radius of convergence of a series and how it relates to the Taylor series expansion of ln(x) around a=2. The person is concerned about getting an infinite radius of convergence, which would mean the series is valid everywhere. However, they later realize their error and apologize for the misunderstanding.
  • #1

nomadreid

Gold Member
1,662
203
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?
 
Mathematics news on Phys.org
  • #2
nomadreid said:
What am I doing wrong?

We can't answer that unless you write your calculations.
 
  • #3
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.
 

1. What is the radius of convergence for ln(x) around a=2?

The radius of convergence for ln(x) around a=2 is 2. This means that the series will converge for all values of x within a distance of 2 from the center, which is a=2.

2. How is the radius of convergence determined for ln(x)?

The radius of convergence for ln(x) is determined by first finding the interval of convergence, which is the distance from the center that the series will converge. This interval is then divided by 2 to get the radius of convergence.

3. Can the radius of convergence for ln(x) be negative?

No, the radius of convergence for ln(x) cannot be negative. The radius of convergence is always a positive value, as it represents a distance from the center.

4. What happens to the series when x is outside of the radius of convergence for ln(x)?

When x is outside of the radius of convergence for ln(x), the series will not converge. This means that the series will either diverge or oscillate, depending on the specific values of x.

5. How does the value of a affect the radius of convergence for ln(x)?

The value of a has a direct effect on the radius of convergence for ln(x). As a increases, the radius of convergence will decrease, and as a decreases, the radius of convergence will increase.

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

Replies
14
Views
236
Replies
3
Views
873
Replies
2
Views
665
Replies
9
Views
1K
Replies
5
Views
2K
Replies
16
Views
902
Replies
10
Views
1K
Replies
7
Views
1K

Back
Top