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Harmonic Sum Approximation

Problem

Hn = 1 + 1/2 + 1/3 + ... + 1/n is defined as the nth Harmonic number.

  1. Prove that Hn approximately ln(n) + 1/(2n) + k, where 0.5 less than k less than 1.
  2. By using k = 0.5772, estimate the sum of the first one hundred Harmonic numbers.
Problem ID: 209 (17 Feb 2005)     Difficulty: 4 Star

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