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Find the value of (.^(10)C(10))+(.^(10)C...

Find the value of `(.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9))`.

Text Solution

Verified by Experts

The correct Answer is:
`10 xx 2^(9)`
`(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"...."+.^(10)C_(9))`
`= 10.^(100)C_(0) + 9.^(10)C_(1)+8.^(10)C_(2)+"...."+.^(10)C_(9)`
`= .^(10)C_(1) +2.^(10)C_(2)+3.^(10)C_(3)+"...."+10.^(10)C_(10)`
`= underset(r=1)overset(10)sum..^(10)C_(r) = 10 underset(r=1)overset(10)sum.^(9)C_(r-1)=10 xx 2^(9)`
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