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
