# Radius of Convergence of the Power Series

Complex Variable

Radius of Convergence of the Power Series

∞ ∞

Theorem:- ∑ anzn is a power series and ∑ nanzn - 1 is the power series obtained

n=0 n=0

by differentiating the first series term by term.

Then the derived series has the same radius of convergence as the original series.

See the attached file.

Â© BrainMass Inc. brainmass.com November 30, 2021, 12:21 am ad1c9bdddfhttps://brainmass.com/math/basic-algebra/radius-of-convergence-of-the-power-series-37244

#### Solution Preview

Complex Variable

Radius of Convergence of the Power Series

...

#### Solution Summary

This solution is comprised of a detailed explanation of the radius of convergence of the

∞

power series ∑ anzn.

n=0

It contains step-by-step explanation for the following problem:

∞ ∞

Theorem:- ∑ anzn is a power series and ∑ nanzn - 1 is the power series obtained

n=0 n=0

by differentiating the first series term by term.

Then the derived series has the same radius of convergence as the original series.

Solution contains detailed step-by-step explanation.