Question: Use the fact that, for a decreasing integrable function, f, to show that, for the nth harmonic number, H n , ln n H

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, Hn, 

ln n ≤ Hn ≤ 1 + ln n.

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

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