The Maclaurin series of is (1+kx)=kx- k^ 2 x^ 2 2 + k^ 3 x^ 3 3 -

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

Problem

The Maclaurin series of

p(x)=\ln(1+kx)

\ln(1+kx)=kx-\frac{k^{2}x^{2}}{2}+\frac{k^{3}x^{3}}{3}-\cdots.

If the coefficient of

x^{2}

in this series is

-\dfrac{9}{2}

and

k>0

, what is the value of

k

? (a)

9

(b)

3

(c)

\dfrac{3}{2}

(d)

\sqrt{\dfrac{9}{2}}