let: $$C_n = \left|\left(a-\frac{(n-b)^n}{n^n}\right)\right|$$ I want to find for which values $C_n$ is decreases monotonically in other words: when $C_{n+1} < C_n$?
I started writing it but it was so hard since sometimes $n$ is even sometimes it's not and sometimes it's negative and others it's positive.