USING R CODE

$1$ Calculate the sum ${\displaystyle \underset{j=0}{\overset{n}{}}}{r}^j,$ where $r$ has been assigned the value $1\mathrm{.}08,$

and compare with $\frac{1-r^{n+1}}{1-r},$ for $n=10,20,30,40.$ Repeat for

$r=1\mathrm{.}06.$

$2$ Referring to the above question, use the quick formula to compute

${\displaystyle \underset{j=0}{\overset{n}{}}}{r}^j,$ for $r=1\mathrm{.}08,$ for all values of $n$ between $1$ and $100.$ Store

the $100$ values in a vector.