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Prove the inequalities : (a) n! lt ((n...

Prove the inequalities :
(a) `n! lt ((n+1)/2)^(n)` for a natural `n gt 1`:
(b) `1/3 .3/4. 5/6 ......(2n-1)/(2n) lt (1)/sqrt(2n+1)`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2n+1)`
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Knowledge Check

  • For natural number n , 2 ^(n) ( n -1)! lt n ^(n), if

    A
    `n lt 2`
    B
    `n gt 2`
    C
    `n ge 2`
    D
    Never

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