T$4$D$.2$ Prove equation T$4\mathrm{.}32.[$You can do this a number of ways. The most direct is by long division. If you know that method, divide $1$ by $1-x$ and see what the pattern becomes. Alternatively, you can prove by induction that

$1+x+x^2+$dots$+x^n=\frac{1-x^{n+1}}{1-x}$

and then take the limit as $n$ goes to infinity. Yet another way is to expand $(1-x{)}^{-1}$ in a Taylor series about $x=0,$ if you know how to do that.$]$