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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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Answer» `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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