How does one prove anything by induction? Can you say which part of the general method is problematic in this case? – 2012-12-16
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Should there be some restriction on the value of $n$, because the statement is false for $n = 1, 2, 3$? – 2012-12-16
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The OP probably intended for $n \geq 4$. – 2012-12-16
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@cardinal yes, of course! – 2012-12-16
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I edited it sorry it deserved a -1.... – 2012-12-16
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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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Related Posts
[6581] How to prove $a^n < n!$ for all $n$ sufficiently large, and $n! \leq n^n$ for all $n$, by induction?
[1140396] Prove by induction that $n^2
[764808] Hint in Proving that $n^2\le n!$