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Prove that (n !)^2 < n^n n! < (2n)!, for...

Prove that `(n !)^2` < `n^n n!` < `(2n)!`, for all positive integers n.

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Given,
`(n!)2<=n^n(n!)`part =`n<=n`
=`(n−1)<=n`
=`(n−2)<=n`
`∴n(n−1)(n−2)......1<=n.n.n......n `times
`n!<=n^n`
multiply both sides by n!, we get:
...
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