Without using calculus (as in the previous exercise), show that, if n is a power of 2

Question:

Without using calculus (as in the previous exercise), show that, if n is a power of 2 greater than 1, then, for H_n, the nth harmonic number,

H_n ≤ 1 + H_n/2

Use this fact to conclude that Hn ≤ 1 + [log n], for any n ≥ 1.

Data From Previous Exercise

Use the fact that, for a decreasing integrable function, f,

cb+1 b f(x)dx < f (x)dx, r=a r=a-1 2=a

to show that, for the nth harmonic number, H_n,

ln n ≤ H_n ≤ 1 + ln n.

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Step by Step Answer:

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Algorithm Design And Applications

ISBN: 9781118335918

1st Edition

Authors: Michael T. Goodrich, Roberto Tamassia

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Question Posted: Aug 10, 2020 06:01 AM

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Without using calculus (as in the previous exercise), show that, if n is a power of 2

Question:

cb+1 b f(x)dx < f (x)dx, r=a r=a-1 2=a

Step by Step Answer:

If n is a power of 2 greater than 1 then there are n2 terms in the differe...View the full answer

Algorithm Design And Applications

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