Thread: Show that : n = E (n * (1 + LOG ((n) -LOG (1 + n)) + 1) with n strictly positive integer

HI,


Show that n = E ((n * (1 + LOG (n) -LOG (1 + n)) + 1)
With n is a strictly positive integer
and E is an integer (The ENT function on Excel).

Check your parentheses. Should it be (log(n)-log(n+1))?

tanks you n = E ((n * (1 + LOG (n) -LOG (1 + n)) + 1)

I have to check that n<=((n * (1 + LOG (n) -LOG (1 + n)) + 1) <n+1 to define the integer part
but n#((n * (1 + LOG (n) -LOG (1 + n)) + 1).


et and I can demonstrate that n<((n * (1 + LOG (n) -LOG (1 + n)) + 1) <n+1 So I can't define the integer part.

By definition if n<x<n+1 then the integer part of x is n. Therefore you are done.