The Cauchy condensation test The Cauchy condensation test says: Let {a,} be a nonincreasing sequence (a, 2 an÷1 for all n) of positive terms that converges to 0. Then Ea, converges if and only if E2"az- converges. For example, E(1/n) diverges because E2" - (1/2") = E1 diverges. Show why the test works. %3D
The Cauchy condensation test The Cauchy condensation test says: Let {a,} be a nonincreasing sequence (a, 2 an÷1 for all n) of positive terms that converges to 0. Then Ea, converges if and only if E2"az- converges. For example, E(1/n) diverges because E2" - (1/2") = E1 diverges. Show why the test works. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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