The value of sum(r=0)^(10)(r)^(20)Cr is ...

The value of `sum_(r=0)^(10)(r)^(20)C_r` is equal to `20(2^(18)+^(19)C_(10))` b. `10(2^(18)+^(19)C_(10))` c. `20(2^(18)+^(19)C_(11))` d. `10(2^(18)+^(19)C_(11))`

A

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

B

`10(2^(18)+.^(18)C_(10))`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:

A

`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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