Question about the Harmonic Number Function

[The Student]

I should only get help on this because the question is for marks.

The question asks us to show how the sum of 1/i from i = 1 to n = any natural number is he same thin as the definite integral of (1-x^n)/(1-x) from 0 to 1.

 

[ksdhart]

I'd start by performing polynomial long divison (see here if you need a refresher) on (1 - x^n)/(1 - x). If needed, you might try it with a simpler case, say where n=5, to start. What do you get? And what happens if you take the integral of that result from x=0 to 1?

 

[The Student]

I'd start by performing polynomial long divison (see here if you need a refresher) on (1 - x^n)/(1 - x). If needed, you might try it with a simpler case, say where n=5, to start. What do you get? And what happens if you take the integral of that result from x=0 to 1?

Thanks!