Chapter 10, Problem 125CRE

To determine

To verify $T_n(x)=1+x+x^2+\mathrm{...}+x^n$ is the $n^{th}$ Maclaurin polynomial of $f(x)=\frac{1}{1-x}$

And by substitution, show that $n^{th}$ Maclaurin polynomial for $f(x)=\frac{1}{1-\frac{x}{4}}$ is $T_n(x)=1+\left(\frac{x}{4}\right)+{\left(\frac{x}{4}\right)}^2+\mathrm{...}+{\left(\frac{x}{4}\right)}^n$

And calculate $n^{th}$ Maclaurin polynomial for $g(x)=\frac{1}{1+x}$