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Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)), then the value of (100t_(100))/(S_(100)) is

Answer»

`1`
`2`
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Solution :`(b)` `S_(100)=(0)/(('^(100)C_(0))^(5))+(1)/(('^(100)C_(1))^(5))+(2)/(('^(100)C_(2))^(5))+....+(100)/(('^(100)C_(100))^(5))`......`(1)`
ALSO `S_(100)=(100)/(('^(100)C_(0))^(5))+((100-1))/(('^(100)C_(1))^(5))+((100-2))/(('^(100)C_(2))^(5))+....+(0)/(('^(100)C_(100))^(5))`......`(2)`
`:.` On adding `(1)` and `(2)`, we get
`2S_(100)=100t_(100)`
`implies(100t_(100))/(S_(100))=2`


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