Using the binomial series for $(1+x)^r = \sum_{n=0}^{\infty} \binom{r}{n} x^n$, where $\binom{r}{n} = \frac{r(r-1)\cdots(r-n+1)}{n!}$, find the first three nonzero terms of the Maclaurin series for $f(x) = \sqrt[3]{1+x}$ on its interval of convergence.