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Asked Feb 21, 2020
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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
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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

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