Let . Which of the following lists the first four nonzero terms of the Maclaurin…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

f(x)=\dfrac{2x}{1-4x}

. Which of the following lists the first four nonzero terms of the Maclaurin series for

f

? (a)

2x+4x^{2}+8x^{3}+16x^{4}+\cdots

(b)

2x+8x^{2}+32x^{3}+128x^{4}+\cdots

(c)

2x-8x^{2}+32x^{3}-128x^{4}+\cdots

(d)

2x+8x^{2}+16x^{3}+32x^{4}+\cdots