expand the function f(z)=1/z^2 in a taylors series around z=1. What is the radius of convergence?

Attempted soln: Since 1/z^2 has a singularity at 0, isnt the radius of convergence just R=1-0 ?

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- March 25th 2010, 02:10 PMstumped765taylors series, complex variables
expand the function f(z)=1/z^2 in a taylors series around z=1. What is the radius of convergence?

Attempted soln: Since 1/z^2 has a singularity at 0, isnt the radius of convergence just R=1-0 ? - March 25th 2010, 05:04 PMtonio
- March 25th 2010, 06:55 PMstumped765
i found the taylor expansion to be

SUM(n=0 to infinity) (-1)^n (n+1)*(z-1)^n

does that sound right? - March 25th 2010, 07:07 PMtonio
- March 29th 2010, 01:40 PMstumped765
is there any way to find radius of convergence without using the ratio/comparison tests?

- March 29th 2010, 01:58 PMlilaziz1
You could do this: