Question: Let a n = H n ln n, where H n is the nth harmonic number: H = 1 + 2 + + 3

Let an = Hn − ln n, where Hn 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

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

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