how do you derive using geometric series to derive a power series for f(x)=1/1-x? How do you find the radius of convergence for this power series?

how do you derive using geometric series to derive a power series for f(x)=1/1-x? How do you find the radius of convergence for this power series?

With this answer, how do you use this to derive a power series for the next function f(x)=1/1+(x^2)? what is the radius of convergence for this power series?

How can you integrate the power series that results from f(x)=1/1+(x^2) to derive a pwer series for f(x)=tan^-1(x)? What is the radius of convergence and the first 4 terms for the power series in sigma notation?