How do you find the power series and the interval of convergence for f(x)=1/(1-x^2)

Question

How do you find the power series and the interval of convergence for f(x)=1/(1-x^2)



Answer 1

The easiest way to find the power series is by long division.

The power series is actually a geometric series: 1+ x² + x⁴ _{+ ....}

If you write expression for the sum of the finite geometric series, you will immediately see that the region of convergence is |x|<1.