Let

$f(x)=\frac{1}{(4+x{)}^5}$

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.$)$

$\frac{1}{(4+x{)}^5}={\displaystyle \underset{n=0}{\overset{}{}}}(\frac{k}{n})$

where $k=0$

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

$\frac{1}{(4+x{)}^5}$~~

$$

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

$R=$

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