For , which of the following series equals…

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

Problem

For

|x|<1

, which of the following series equals

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

? (a)

\displaystyle \sum_{n=0}^{\infty}x^{3n+1}

(b)

\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{3n}

(c)

\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{3n+1}

(d)

\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{n+1}