This is from the book

How to think like a Mathematician,How can I prove the inequality

7√7!<8√8!without complicated calculus? I tried and finally obtained just 17⋅ln(7!)<18⋅ln(8!)

**Answer**

Your inequality is equivalent to

(7!)8<(8!)7

divide it by (7!)7, and get

7!<87

and this is clear, since 1⋯7<8⋯8

**Attribution***Source : Link , Question Author : Gwydyon , Answer Author : Crostul*