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The value of sum_(k=0)^(7)[(((7),(k)))/(((14),(k)))sum_(r=k)^(14)((r ),(k))((14),(r ))], where ((n),(r )) denotes "^(n)C_(r ) is |
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Answer» `6^(7)` `=sum_(k=0)^(7)(('^(7)C_(k))/(14!)xxk!(14-k)!sum_(r=k)^(14)(r !)/(k!(r-k)!)*(14!)/(r!(14-r)!))` `=sum_(k=0)^(7)('^(7)C_(k)sum_(r=k)^(14)'^(14-k)C_(r-k))` `=sum_(k=0)^(7)'^(7)C_(k)*2^(14-k)=2^(14)sum_(k=0)^(7)'^(7)C_(k)((1)/(2))^(k)` `=2^(14)*(1+(1)/(2))^(7)=6^(7) gt 7^(6)` |
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