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If S(n) = (.^(n)C(0))^(2) + (.^(n)C(1))^...

If `S_(n) = (.^(n)C_(0))^(2) + (.^(n)C_(1))^(2) + (.^(n)C_(n))^(n)`, then maximum value of `[(S_(n+1))/(S_(n))]` is `"_____"`.
(where `[*]` denotes the greatest integer function)

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Verified by Experts

The correct Answer is:
3
`S_(n) = .^(2n)C_(n)`
`rArr (S_(n+1))/(S_(n)) = (.^(2n+2)C_(n+1))/(.^(2n)C_(n)) = ((2n+2)(2n+1))/((n+1)(n+1))`
`= (2(2n+1))/(n+1)=4-(2)/(n+1)`
`:. [(S_(n+1))/(S_(n))]_("max") = 3`
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