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.

Printable View

- Mar 17th 2013, 04:51 PMOtto45help with proof involving harmonic sequence
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. - Mar 17th 2013, 06:17 PMchiroRe: help with proof involving harmonic sequence
Hey Otto45.

What is the definition of H_n? - Mar 17th 2013, 06:35 PMGusbobRe: help with proof involving harmonic sequence
Judging by the title and the question, should be the partial sum of the harmonic series.

- Mar 17th 2013, 08:48 PMjohngRe: help with proof involving harmonic sequence
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:

Attachment 27582