MHB Convergence Condition for Applying Ratio Test to Power Series

alexmahone · Feb 23, 2012

Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

Dustinsfl · Feb 23, 2012

Alexmahone said:

Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

I think it can always be applied. Other test just may be easier for a given power series.

Prove It · Feb 23, 2012

Alexmahone said:

Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

You actually should always do the ratio test on the series of ABSOLUTE VALUES, to prove absolute convergence (i.e. to show the series is bounded both above and below by the series of absolute values and the negative of the series of absolute values).

MHB Convergence Condition for Applying Ratio Test to Power Series

Thread 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

Similar threads

Hot Threads

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

I How are the following three definitions subtly different?

I Convergence not defined by any metric

I Confused by proof in Hocking and Young

I Homemorphism in quotient topology

Recent Insights

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

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers