1.

The value of sum_(r=0)^(10) (r)""^(20)C_(r) is equal to

Answer»

`20(2^(18)+.^(19)C_(10))`
`10(2^(18)+.^(18)C_(10))`
`20(2^(16)+.^(19)C_(11))`
`10(2^(18)+.^(19)C_(11))`

SOLUTION :`UNDERSET(R=0)overset(10)sum(r).^(20)C_(r) = underset(r=1)overset(10)sum20 xx .^(19)C_(r-1)`
`= 20(.^(19)C_(0) + .^(19)C_(1) + "......"+ .^(19)C_(10))`
`= 20 (.^(19)C_(0) +.^(19)C_(1) + "......" + .^(19)C_(10))`
`= 20(1/2 xx 2^(10) + .^(19)C_(10))`
`= 20(2^(18)+.^(19)C_(10))`


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