Thread: help with proof involving harmonic sequence

Prove that:
H₁+H₂+...+H_n = (n+1)H_n-n
I'm totally lost on this problem. I know it involves using induction in some way, but I have no clue how to tackle it.

Hey Otto45.

What is the definition of H_n?

Judging by the title and the question, should be the partial sum of the harmonic series.

Hi Otto,

Undoubtedly you know about integration by parts which applies to the integral of a product. The discrete analog to this is summation by parts which applies to the sum of a product. One proof of your equation uses this summation by parts. Here it is: