Find the first four terms of the binomial series for the given function.
-$$( 1 + 5 x ) ^ { 1 / 3 }$$
A) $1 + \frac { 5 } { 3 } x - \frac { 25 } { 9 } x ^ { 2 } + \frac { 625 } { 81 } x ^ { 3 }$
B) $1 + \frac { 5 } { 3 } x + \frac { 25 } { 9 } x ^ { 2 } + \frac { 125 } { 27 } x ^ { 3 }$
C) $1 + \frac { 5 } { 3 } x - \frac { 25 } { 9 } x ^ { 2 } + \frac { 125 } { 27 } x ^ { 3 }$
D) $1 - \frac { 5 } { 3 } x + \frac { 25 } { 3 } x ^ { 2 } - \frac { 625 } { 81 } x ^ { 3 }$

Question

Quizplus · Accepted Answer

The binomial series for $ ( 1 + 5 x ) ^ { 1 / 3 } $ is given by$$( 1 + 5 x ) ^ { 1 / 3 } = 1 + \frac { 1 } { 3 } ( 5 x ) - \frac { 1 } { 2 \cdot 3 } ( 5 x ) ^ { 2 } + \frac { 1 } { 3 \cdot 4 } ( 5 x ) ^ { 3 } - \cdots$$The first four terms of this series are$$1 + \frac { 5 } { 3 } x - \frac { 25 } { 9 } x ^ { 2 } + \frac { 625 } { 81 } x ^ { 3 }$$

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