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Prove that ""^(n)C(3)+""^(n)C(7) + ""...

Prove that
`""^(n)C_(3)+""^(n)C_(7) + ""^(n)C_(11) + ...= 1/2{2^(n-1) - 2^(n//2 )sin"" (npi)/(4)}`

A

`1/2{2^(n-1)-2^(n//2)"sin"(npi)/(4)}`

B

`1/2{2^(n-1)+2^(n//2)"sin"(npi)/(4)}`

C

`1/2{2^(n+1)-2^(n//2)"sin"(npi)/(4)}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
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Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) + .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

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VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
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