Identify the interval of convergence of a power series
$\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }$
A) $- 3

Question

Identify the interval of convergence of a power series
$\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }$ 
A) $- 3 < x < 3$
B) $- 1 < x < 1$
C) $- \frac { 1 } { 3 } < x < \frac { 1 } { 3 }$
D) $0 < x < 3$
E) $- \frac { 1 } { 6 } < x < \frac { 1 } { 6 }$

Quizplus · Accepted Answer

The series is a geometric series with common ratio $-3x$. For convergence, $|-3x| < 1$ which simplifies to $-\frac{1}{3} < x < \frac{1}{3}$.

Identify the Interval of Convergence of a Power Series ∑n=1∞(−3)nnxn−1\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }∑n=1∞​(−3)nnxn−1

Identify the Interval of Convergence of a Power Series $\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }$