Question

Suppose that the radius of convergence of the power series

SUMcn x^n is R.
What is the radius of convergence of the power series

SUMcn x^(4n)?

Answer 1

The radius of convergence for the power series ∑cn x^(4n) is also R.

Step-by-step explanation:

To find the radius of convergence for the power series ∑ncn x^4n, we need to determine the values of x for which the series converges.

The radius of convergence for the power series ∑cn x^n is R.

Since x4n is always positive, the convergence of the series will be determined by the convergence of the series:

=> ∑ncn x^n.

Hence, the radius of convergence for the power series ∑ncn x^4n is also R.