Series Summation: Does the Ratio Test Determine Convergence or Divergence?

barksdalemc · Oct 17, 2006

I have this HW problem: Suppose Un and Vn are sequences of positve numbers such that the ratio of Un+1/Un will always we less than Vn+1/Vn. Show that 1) If Vn converges Un converged and 2) If Un diverges, Vn diverges.

I did the first part by showing that for any n, the ration of Un/Vn is decreasing and if lim of the ratio=M then Un=MVn.

Stuck on the second part.

barksdalemc · Oct 17, 2006

ration=ratio

Series Summation: Does the Ratio Test Determine Convergence or Divergence?

Discussion

Hi! Can someone explain about Differential Equations?

Investigating the real roots of a cubic equation

Deriving spatial derivatives

What does "compute Aut(G)" mean?

J_1(x) = (x^2/10)*(J_1(x) + J_3(x)) How to solve?

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

Series Summation: Does the Ratio Test Determine Convergence or Divergence?

Discussion

Similar threads

Undergrad How Does the Ratio Test Determine Convergence in Power Series?

Undergrad How Does the Ratio Test Prove Series Convergence?

Undergrad Can the ratio test determine if an infinite series converges or not?

Undergrad Does the Ratio Test guarantee convergence for this infinite series?