Question

Determine a power series representation for f(x)=4/(1+x^2) using the "pseudogeometric" approach; also determine the interval of convergence.

Answer 1

\[
\frac 1{1+u}=\sum_{n=0}^\infty (-1)^n u^n, \quad|u| <1
\]
replace u by x^2 and you are done

Answer 2

\[
\frac 1{1+x^2}=\sum_{n=0}^\infty (-1)^n x^{2n}, \quad|x| <1
\]

Answer 3

is that the pseudogeometric way?