Let a n = H n ln n, where H n is the nth harmonic number:

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Let a_n= H_n − ln n, where H_n is the nth harmonic number:

H = 1 + 2 + + 3 n+1 Sa+s (a) Show that an 0 for n 1. Hint: Show that Hn > dx X n

(b) Show that {an} is decreasing by interpreting an - an+1 as an area. (c) Prove that lim an exists. n0 This

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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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Let a n = H n ln n, where H n is the nth harmonic number:

Question:

H₂ = 1 + 2 + + 3 n+1 Sa+s (a) Show that an ≥ 0 for n ≥ 1. Hint: Show that Hn > dx X n

Step by Step Answer:

a Since the function y is decreasing the left endpoint approximation to the ...View the full answer

Calculus

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