Let

$f(x)=\sqrt[3]{243x}$

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 of $n=0,$ and any coefficient of the summation should be included within the sum itself.$)$

$\sqrt[3]{243z}={\displaystyle \underset{n=0}{\overset{}{}}}(\frac{k}{n})$

$$

where $k=$

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

$\sqrt[3]{243}$

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

$R=$

$$