How do you use the binomial series to expand (1+2x)^-3 ?

$\sum {a}_{n} {x}^{n - 1}$, through n = 1, 2, 3.., with ${a}_{1} = 1 \mathmr{and} {a}_{n} = - 2 \left(\frac{n + 2}{n}\right) {a}_{n} - 1$, n=2, 3, 4,..., for $| x | < \frac{1}{2}$.
Use (1+kx)^(-m)=1-m(kx)/1!+m(m+1)(kx)^2/(2!)+...+(-1)^(n-1)(m(m+1)(m+2)...(m+n-1))(kx)^n/(n!)+..., for $| k x | < 1$.
$= \sum {a}_{n} {x}^{n - 1}$, where${a}_{1} = 1 \mathmr{and} {a}_{n} = - k \left(\frac{m + n - 1}{n}\right) {a}_{n - 1}$