Radius of convergence: 1/(1+x^2) about 1, using only real analysis

[pcvt]

I've seen this thread:
https://www.physicsforums.com/showthread.php?t=297842

and that is the exact question I need to to answer.

What is the radius of convergence of 1/(1+x^2) expanded about x_0=1?

The problem is, I can only use an argument in real analysis.

I see the answer is sqrt(2), but I cannot get that answer.

I've tried a lot of little manipulations to get different geometric series but I can't seem to get it.

Thanks

 

[deluks917]

What is the taylor series? What tests did you try? It might be easier to find the radius of convergence of 1/(1+x) about 1.

 

[pcvt]

I don't see an easy formula for the nth derivative so I'm not sure how to proceed in that direction

 

[deluks917]

I didn't do 1/(1+x^2) but there is nice form of the nth derivative of 1/(1+x)

 

[pcvt]

Do you mean I can use that to get a taylor series for my function