Let for . Which of the following is the Maclaurin series for valid for…

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

Problem

Let

f(x)=\displaystyle\sum_{n=0}^{\infty} \dfrac{x^{\,n+2}}{n+2}

for

|x|<1

. Which of the following is the Maclaurin series for

f'(x)

valid for

|x|<1

? (a)

\displaystyle \sum_{n=0}^{\infty} \dfrac{x^{\,n+1}}{n+2}

(b)

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

(c)

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

(d)

\displaystyle \sum_{n=0}^{\infty} x^{\,n+2}