The identity holds for

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

Problem

The identity

\dfrac{1}{(1-x)^{2}}=\sum_{n=0}^{\infty}(n+1)x^{n}

holds for

|x|<1

. Using the first four non-zero terms of this series, which of the following is the best approximation of

\dfrac{1}{(1-\frac13)^{2}}

? (a)

2.444

(b)

2.000

(c)

2.148

(d)

2.250