(Requires calculus) Let Hn be the nth harmonic numberShow that Hn is O(log n). [Hint: Firs...

(Requires calculus) Let Hn be the nth harmonic number

Show that Hn is O(log n). [Hint: First establish the inequality

by showing that the sum of the areas of the rectangles of height 1/j with base from j − 1 to j. for j = 2, 3,..., n, is less than the area under the curve y = 1/x from 2 to n.]