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)?

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asked Aug 6, 2024 72.3k views

1 Answer

Adeelmahmood · Answer 1 · 2024-08-11T09:41:32+0000

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

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.