Prove that the sum of n harmonic numbers H_1 + H_2 + ... + H_n = (n+1)H_n - n

Prove that the sum of n harmonic numbers H_1 + H_2 + ... + H_n = (n+1)H_n - n

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What do you define as a harmonic number? \(H_n= \frac{1}{n}\)?

H_n =1+ 1/2 + 1/3 + ... 1/n

H_n is the actual sum from k=1 to n of 1/k

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