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The value of (.^(21)C(1) - .^(10)C(1)) +...

The value of `(.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + "…." + (.^(21)C_(10) - .^(10)C_(10))` is

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Verified by Experts

The correct Answer is:
5151
Here `T_(r) = (r^(.1001)C_(r))/(.^(100)C_(r-1))= (r.(1001-r+1))/(r) = 102 -r`
`:.` Given sum `= underset(r=1)overset(101)sum(102-r)`
`= 101+100+99+"...."+2+1`
`=5151`
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CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
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