Find the first four terms of the binomial series for the given function.
-$$( 1 + 4 x ) ^ { - 1 / 2 }$$
A) $1 - 2 x + 6 x ^ { 2 } - 20 x ^ { 3 }$
B) $1 - 2 x - 12 x ^ { 2 } - 20 x ^ { 3 }$
C) $1 - 2 x + 6 x ^ { 2 } - 30 x ^ { 3 }$
D) $1 - 2 x + 6 x ^ { 2 } - 10 x ^ { 3 }$

Question

Quizplus · Accepted Answer

The binomial series expansion for $(1 + ax)^n$ where $n$ is any real number is given by $(1 + ax)^n = 1 + n(ax) + \frac{n(n-1)}{2!}(ax)^2 + \frac{n(n-1)(n-2)}{3!}(ax)^3 + \cdots$. For $(1 + 4x)^{-1/2}$, $a = 4$ and $n = -1/2$, so the first four terms are $1 - 2x + 6x^2 - 20x^3$.

Find the First Four Terms of the Binomial Series for the Given