1.

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

Answer»

`"^(1000)C_(11)-12`
`"^(1000)C_(11)+12`
`"^(900)C_(11)-12`
`"^(1000)C_(989)`

SOLUTION :`(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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