Which algebraic rewrite of the function places it in a form suitable for expressing…

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

Problem

Which algebraic rewrite of the function

f(x)=\dfrac{1}{1+3x}

places it in a form suitable for expressing

f

as a power series centered at

x=0

? (a)

\displaystyle \frac{1}{1-3x}

(b)

\displaystyle \frac{1}{1-\bigl(-x/3\bigr)}

(c)

\displaystyle \frac{1}{1-(-3x)}

(d)

\displaystyle \frac{1}{3}\,\frac{1}{1+x}