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The value of ((C(1))/(C(0))+2(C(2))/(C...

The value of
`((C_(1))/(C_(0))+2(C_(2))/(C_(1))+3(C_(3))/(C_(2))+"......"+10(C_(10))/(C_(9)))`
(where `C_(r) = .^(10)C_(r)`), is `11lambda`, then value of `lambda` is

A

`1`

B

`2`

C

`4`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
D
`(.^(n)C_(r))/(.^(n)C_(r-1)) = (n-r+1)/(r)`
`rArr (r^(n)C_(r))/(.^(n)C_(r-1)) = n - r + 1 = 11 - r (n = 10)`
`:. ((C_(1))/(C_(0)) + 2(C_(3))/(C_(2)) + 3 (C_(2))/(C_(1)) +"……"+10(C_(10))/(C_(9)))`
`= (10 + 9 + "……"+ 1) = (10(11))/(2) = 55`
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