plot in MATLAB the original function $f(x)=\frac{1}{1-x},$ and the partial sums

$f_N(x)={\displaystyle \underset{n=0}{\overset{N}{}}}{x}^n,$

for $N=1,4,7,10,$ for $-2x0\mathrm{.}5$ with $1000$ query points. The observation to

note is how close the curves are for the I.$O.C.),$ and how they

stray away from $\frac{1}{1-x}$ for the I.$O.C.).$