$[0\mathrm{.}68/1$ Points$]$

SCALCET$8$M $11\mathrm{.}9\mathrm{.}040.\frac{2}{3}$ Submissions Used

$($a$)$ Starting with the geometric series ${\displaystyle \underset{n=0}{\overset{}{}}}{x}^n,$ find the sum of the series

${\displaystyle \underset{n=1}{\overset{}{}}}n{x}^{n-1},|x|<mn>1</mn>$

$($b$)$ Find the sum of each of the following series.

$($i$){\displaystyle \underset{n=1}{\overset{}{}}}n{x}^n,|x|<mn>1</mn>$

$$

$($ii$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{n}{9^n}$