Power series and uniform convergence.

MissC · May 20, 2017

Hi.
I have this power serie (2^n/n)*z^n that runs from n=1 to infinity, and I have to show whether it's uniform konvergence on [-1/3, 1/3] or not.

I hope someone can help me with this.

HallsofIvy · May 20, 2017

It is fairly standard to use the "ratio test" or "root test" to determine convergence of a power series. And I presume you know that "if a power series converges on a closed and bounded interval, then it converges uniformly there."

Power series and uniform convergence.

Discussion

Graduate A nice YouTube channel about all things Riemann Zeta

Undergrad What is "x" in this definition of a basis?

Graduate Knots In 4D

Graduate Zeros of functions analytic in 2 variables

Undergrad A differential geometry question from continuum mechanics

Graduate Nonautonomous Lie derivative

Graduate Shauder basis for Hilbert spaces

Undergrad No structure in ##(d,x)## in ##\textbf{Met*}(X)## is admissible

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Power series and uniform convergence.

Discussion

Similar threads

Undergrad About convergence of complex power series on the circle ##|z - z_0|=r##

Undergrad Riemann integrability and uniform convergence

Undergrad Uniform convergence of difference quotient in higher dimensions

Sequence of functions : pointwise & uniform convergence

Uniform convergence - Length of graph

Uniform convergence of a complex power series on a compact set

Undergrad Pointwise and Uniform Convergence

Undergrad Uniform convergence and pointwise convergence

Graduate Uniform Convergence of Power Series

Undergrad Uniform convergence of family of functions with continuous index