$(6$ points$)$ Suppose that

$\frac{2}{(1-x^3)}={\displaystyle \underset{n=0}{\overset{}{}}}{c}_n{x}^n$

Find the following coefficients of the power series.

$c_0=$

$c_1=$

$c_2=$

$c_3=$

$c_4=$

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Find the radius of convergence $R$ of the power series.

$R=$

$$