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Proving an inequation with induction

Hi, I need help with this simple (I think) inequality:

I need to prove with induction that for each natural number n the following inequation is true: (see the "small" image below)

I tried to use the Latex system but I keep getting errors for some reason...

Thanks in advance

Re: Proving an inequation with induction

The LaTeX code:

[TEX]\left( {\frac{{n + 1}}{4}} \right)^n \leqslant n![/TEX]

gives

$\displaystyle \left( {\frac{{n + 1}}{4}} \right)^n \leqslant n!$

HINT:

$\displaystyle \left( {N + 1} \right)! = \left( {N + 1} \right)N! \geqslant \left( {\frac{{N + 1}}{4}} \right)\left( {\frac{{N + 1}}{4}} \right)^N $

Re: Proving an inequation with induction

Thanks, I hope that this trick is going to help me.