Math Problem Issue: Deriving 4.12 from 4.11

[matt222]

Homework Statement

It is not a homework but I will call it an homework for me, the problem for math derivation shown in the attached file, it is from the book I use. From equastion 4.11 we have to derive 4.12, in this step i disagree with output result since it should be (n-N/n) not as the book state (N-n/n)? does anyone agree or disagree with this first step?

second thing if we made our answer which is n-N/n is the correct one do you agree that the final output of 4.14 is correct once the assumption made N>>n! in this case I disagree with my answer and agree with the book answer but now how and why he flip the sign once he jump from 4.11 to 4.12 it doesn't make sense!

any help

Homework Equations

The Attempt at a Solution

 

[vela]

In equation 4.11, it looks like the argument of ln should be N-n, not n-N. Since n<N, ln (n-N) would be undefined.