Solution
= Solution
Use the <binomial series> with exponent $1/2$ and argument $-3x$:
$$
(1-3x)^{1/2}=1+\frac12(-3x)
+\frac{(1/2)(-1/2)}{2!}(-3x)^2+O(x^3).
$$
Thus the first three nonzero terms are
$$
\boxed{1-\frac32x-\frac98x^2+O(x^3).}
$$
= Solution
Use the <binomial series> with exponent $1/2$ and argument $-3x$:
$$
(1-3x)^{1/2}=1+\frac12(-3x)
+\frac{(1/2)(-1/2)}{2!}(-3x)^2+O(x^3).
$$
Thus the first three nonzero terms are
$$
\boxed{1-\frac32x-\frac98x^2+O(x^3).}
$$