$$ ((n+1)H_n - (n+1)) + H_{n+1} = (n+2)H_{n+1} - (n+2) $$ I need to prove the above statement.
I would like a hint on this problem regarding harmonic numbers
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discrete-mathematics
induction
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0doesn't merely using the definition of $H_n$ work? – 2010-11-03
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1$H_{n+1}=H_n+1/(n+1)$ – 2010-11-03
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0I should have added that I had gotten that far, but I can't figure what to do with that. – 2010-11-03
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1@Mark: cancel as many terms as you can. – 2010-11-03
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0Do you really need to prove it by induction? In my answer I assumed not. – 2010-11-03
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0It's part of an inductive proof ($H_1+H_2+...+H_n = (n+1)H_n - (n+1)$) – 2010-11-03
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0Thanks for all the help, I've now fully proven the statement. – 2010-11-03