Consider the two power series

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

Problem

Consider the two power series, each centered at

x=-1

: I.

\displaystyle \sum_{n=0}^{\infty} \frac{(x+1)^{n}}{3^{n}}

II.

\displaystyle \sum_{n=1}^{\infty} \frac{n(x+1)^{n}}{5^{n}}

What is the largest interval (centered at

-1

) on which both series converge? (a)

(-6,4)

(b)

[-4,2]

(c)

(-4,2)

(d)

(-5,3)