Let

$f(x)=\sqrt[5]{243-x}$

a$.$ Use the binomial series to write $f$ as a power series involving binomial coefficients.

$($Note that the index variable of the summation is $n,$ it starts at $n=0,$ and any coefficient of the summation should be included within the sum itself.$)$

$\sqrt[5]{243-x}={\displaystyle \underset{n=0}{\overset{}{}}}(\frac{k}{n})5(-\frac{x}{243}{)}^n$

where $k=0$

b$.$ Write the first four terms of the power series expansion from part a$.$

$$

$\sqrt[5]{243-x}$~~

c$.$ State the radius of convergence of the power series.

$R=$

$$