Define for . Which of the following expressions is equal to for…

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

Problem

Define

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

for

|x|\le 1

. Which of the following expressions is equal to

g(x)

for

|x|\le 1

? (a)

\dfrac{1}{2}\ln\bigl(1+x^{2}\bigr)

(b)

x\arctan x-\dfrac{1}{2}\ln\bigl(1+x^{2}\bigr)

(c)

x\arctan x+\dfrac{1}{2}\ln\bigl(1+x^{2}\bigr)

(d)

\arctan x