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The value of "^(12)C(2)+^(13)C(3)+^(14)C...

The value of `"^(12)C_(2)+^(13)C_(3)+^(14)C_(4)+...+^(999)C_(989)` is

A

`"^(1000)C_(11)-12`

B

`"^(1000)C_(11)+12`

C

`"^(900)C_(11)-12`

D

`"^(1000)C_(989)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Since `.^(10)C_(0)+.^(11)C_(1)+.^(12)C_(2)+.^(13)C_(3)+...+.^(999)C_(989)`
`=.^(1000)C_(989)=.^(1000)C_(11)`
(Since, `.^(10)C_(0)=.^(11)C_(0)` and `.^(n)C_(r )+.^(n)C_(r-1)=.^(n+1)C_(r )`)
So, `.^(12)C_(2)+.^(13)C_(3)+.^(14)C_(4)+....+.^(999)C_(989)=.^(1000)C_(11)-12`
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