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# Inequalities

prove that (n!)^2 > n^n

Note by Mishti Angel
3 years, 8 months ago

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It is false for n=1 · 3 years, 8 months ago

Its false for n=2 also · 2 years, 9 months ago

proof: let's take n=1 n! = 1! = 1 (n!)^2 = 1^2 = 1 n^n = 1^1 = 1 then 1 > 1 is false so this expression is false. /* for n=2 n! = 2 n^2 = 2^2 = 4 n^2 = 2^2 = 4 4 > 4 is false · 3 years, 8 months ago

It's true for n = 3, 4, 5, ... · 3 years, 8 months ago

Maybe Mishit think $$(n!)^2\geq n^n$$ · 3 years, 8 months ago