The problem is:

Show that the function

is a monotonically decreasing function when

,

and

,

is a positive integer number.

A proof is as follows (but I cannot understand):

Consider the function

, with

. The first order derivative of

with respect to

is:

Because

when

, so

, and finally, we obtain the function

is monotonically decreasing function. The function

is a special case of

, and we have the proof for the problem.

The above proof is very short, and I cannot understand that. Can everyone give me some ideas?. Thanks in advance.