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Let t(100)=sum(r=0)^(100)(1)/(("^(100)C(...

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 (a) 1 (b) 2 (c) 3 (d) 4

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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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