Chapter 19.4, Problem 56E

(a)

To determine

The first four terms of the expansion of the expression ${\left(1-x\right)}^{-1}$.

(b)

To determine

The expansion of the expression ${\left(1-x\right)}^{-1}$ by long division.

(c)

To determine

The expansion of the expression $1+\frac{A}{1-\frac{{\lambda }_0{}^2}{{\lambda }^2}}$ where $x=\frac{{\lambda }_0{}^2}{{\lambda }^2}$.