a$.$ Find a power series representation for

$f(x)=\frac{8}{(9+x{)}^2}$

by recognizing $f$ as the derivative of another function.

$($Note that the index variable of the summation is $n,$ it starts at $n=1,$ and any coefficient of the summation should be included within the sum itself.$)$

${\displaystyle \underset{n=1}{\overset{}{}}}$

State the radius of convergence for this power series.

$R=$

$q,$

b$.$ Find a power series representation for

$g(x)=\frac{8}{(9+x{)}^3}$

by recognizing $g$ as the derivative of another function.

$($Note that the index variable of the summation is $n,$ it starts at $n=2,$ and any coefficient of the summation should be included within the sum itself.$)$

${\displaystyle \underset{n=2}{\overset{}{}}}$

State the radius of convergence for this power series.

$R=$

c$.$ Find a power series representation for

$h(x)=\frac{8}{(9+x{)}^4}$

by recognizing $h$ as the derivative of another function.

$($Note that the index variable of the summation is $n,$ it starts at $n=3,$ and any coefficient of the summation should be included within the sum itself.$)$

${\displaystyle \underset{n=3}{\overset{}{}}}|||$

State the radius of convergence for this power series.

$R=$