Lilthan5hoda Lilthan5hoda
  • 06-04-2017
  • Mathematics
contestada

Prove that 3n< n! if n is an integer greater than 6.

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LammettHash
LammettHash LammettHash
  • 06-04-2017
Let [tex]n=7[/tex]. Then

[tex]3(7)=21<5040=7![/tex]

Assume the inequality holds for [tex]n=k[/tex], so that [tex]3k<k![/tex]. Then for [tex]n=k+1[/tex], you have, for [tex]k>7[/tex],

[tex]3(k+1)<3k(k+1)<k!(k+1)=(k+1)![/tex]

so the statement is true.
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