For , which of the following is a power-series representation of the function…

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

Problem

For

|x|<1

, which of the following is a power-series representation of the function

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

? (a)

\displaystyle \sum_{n=0}^{\infty}x^{n}

(b)

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

(c)

\displaystyle \sum_{n=1}^{\infty}n x^{n}

(d)

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