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  4. For natural number n, 2n (n-1) ! < nn , if

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Q. For natural number $n, 2^{n } \left(n-1\right) ! < n^{n }$, if

Principle of Mathematical Induction

Solution:

The condition $n, 2^{n } \left(n-1\right) ! < n^{n },$ is satisfied for $n > 2$.