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Prove that ((n + 1)/(2))^(n) gt n!...

Prove that `((n + 1)/(2))^(n) gt n!`

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Verified by Experts

We have
`(1+2+3+4+....+n)/(n) gt (1.2.3.4....n)^(1//n)`
`(m(n+1))/(2))/(n) gt (n!)^(1//n)`
`rArr ((n+1)/(2))^n gt n!`
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