Find the radius of convergence of the power series.

A) -8
B) 1
C) 8
D) -1
E) 0

Question

​Find the radius of convergence of the power series. ​  ​
​
A) ​-8 
B) ​1 
C) ​8 
D) ​-1 
E) ​0

Quizplus · Accepted Answer

To find the radius of convergence, we can use the ratio test:
$$\lim_{n	o\infty}\left|\frac{(n+1)!8^{n+1}}{n!11^n}\cdot\frac{11^n}{8^n(n)!}ight|=\lim_{n	o\infty}\frac{8}{11}\cdot\frac{n+1}{n}= \frac{8}{11}.$$
Therefore, the series converges if $|x|<\frac{11}{8}$ and diverges if $|x|>\frac{11}{8}.$ Thus, the radius of convergence is $\boxed{	ext{(C) }8}$.

​Find the Radius of Convergence of the Power Series

Find the Radius of Convergence of the Power Series