- #1

- 14

- 0

## Homework Statement

Ok, basically I need to show that Ʃ 1/n (between 1 and n) (which is harmonic number) is θ (big theta) of ln(n), which means that is it bounded below and above by this function(upper and lower bound). But I don't quite understand how to prove it.

## Homework Equations

I know that integral of 1/x between 1 and n is ln(n).

## The Attempt at a Solution

I don't think that saying that the integral of 1/x between 1 and n is equal to ln(n) which is approximately equal to Ʃ 1/n (between 1 and n) is enough. But I don't know where to go from here.

need to show:

c1 f(n) <= Ʃ 1/n (between 1 and n) <= c1 f(n)

where f(n) is the ln(n) and c1 and c2 are some constants. What I don't understand is how to find these constants.

Thanks.