Prove that:
H_{1}+H_{2}+...+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.
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: