The function has a Maclaurin series that can be written as

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

Problem

The function

g(x)=\dfrac{1+2x}{1-x}

has a Maclaurin series that can be written as

g(x)=\sum_{n=0}^{\infty}a_n x^n

. Which of the following gives

g(x)

up to and including the

x^{3}

term? (a)

1+2x+2x^{2}+2x^{3}+\cdots

(b)

1+x-x^{2}+x^{3}+\cdots

(c)

1+3x+3x^{2}+3x^{3}+\cdots

(d)

1+3x+6x^{2}+9x^{3}+\cdots