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How does one prove by induction that

$n! > n^2$

for $n \geq 4$

  • 0
    This is not true when n=12012-12-16
  • 4
    How does one prove anything by induction? Can you say which part of the general method is problematic in this case?2012-12-16
  • 0
    Should there be some restriction on the value of $n$, because the statement is false for $n = 1, 2, 3$?2012-12-16
  • 3
    The OP probably intended for $n \geq 4$.2012-12-16
  • 1
    @cardinal yes, of course!2012-12-16
  • 1
    I edited it sorry it deserved a -1....2012-12-16
  • 0
    Related question: [How to prove $a^n < n!$ for all $n$ sufficiently large, and $n! \leq n^n$ for all $n$, by induction?](http://math.stackexchange.com/questions/6581/how-to-prove-an-n-for-all-n-sufficiently-large-and-n-leq-nn-for-al)2012-12-16
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    See also: [Prove by induction that $n^2](http://math.stackexchange.com/questions/1140396/prove-by-induction-that-n2n) and [Hint in Proving that $n^2\le n!$](http://math.stackexchange.com/questions/764808/hint-in-proving-that-n2-le-n)2015-02-09

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