Suppose that the radius of convergence of the power series $\sum _ { n = 0 } ^ { \infty } c _ { n } x ^ { n }$ is $9$ . What is the radius of convergence of the power series $\sum _ { n = 0 } ^ { \infty } c _ { n } x ^ { 2 n }$ .
A) $252$
B) $3$
C) $1$
D) $256$
E) $16$

Question

Quizplus · Accepted Answer

The radius of convergence of $\sum _ { n = 0 } ^ { \infty } c _ { n } x ^ { 2 n }$ is the square root of the original radius of convergence, which is $\sqrt{9} = 3$.

Suppose That the Radius of Convergence of the Power Series ∑n=0∞cnxn\sum _ { n = 0 } ^ { \infty } c _ { n } x ^ { n }∑n=0∞​cn​xn

Suppose That the Radius of Convergence of the Power Series $\sum _ { n = 0 } ^ { \infty } c _ { n } x ^ { n }$