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.