Let H0 = 0 and Hn = 1/1 + 1/2 + ... + 1/n.
Show that, for n > 0, Hn = 1 + (H0 + H1 + ... + Hn−1)/n.
(That is, show that Hn is one greater than the arithmetic mean of the n preceding values, H0 to Hn−1.)

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