Question

How do you find the Maclaurin series of `f(x)=(1-x)^-2` ?

Answer 1

By taking the derivative of a geometric power series,

`f(x)=sum_{n=1}^infty nx^{n-1}`.

Let us look at some details.

Since

`1/{1-x}=sum_{n=0}^infty x^n`,

by taking the derivative,

`1/{(1-x)^2}=sum_{n=0}^infty nx^{n-1}=sum_{n=1}^infty nx^{n-1}`.

I hope that this was helpful.