The following argument proves the divergence of the harmonic series without using the Integral Test. To begin,

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The following argument proves the divergence of the harmonic series 00 =1 1 without using the Integral Test. To begin, assume that the harmonic series converges to a value S.

(a) Prove that the following two series must also converge: 1 1 1+ + +... and 5 3 1 1 + + 2 4 6 + (b) Prove

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 19, 2023 06:28 AM

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The following argument proves the divergence of the harmonic series without using the Integral Test. To begin,

Question:

00 η=1 1/n

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2k1 a For the first series let a21 for k20 and a2k Comparison Test if the harmonic series ...View the full answer

Calculus

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