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)

Answer»


SOLUTION :`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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