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Question

If (1+x)n=C0+C1x+C2x2++Cnxn, then the value of 0r<sn(rs)CrCs is

A
n2[22n3+122n2Cn1]
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B
[22n3122n2Cn1]
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C
n2[22n3122n2Cn1]
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D
[22n3+122n2Cn1]
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Solution

The correct option is C n2[22n3122n2Cn1]
We have, 0r<sn(rs)CrCs

=0r<sn(rnCr)(snCs)

=0r<sn(rnrn1Cr1)(snsn1Cs1) =n20r<sn(n1Cr1)(n1Cs1)

=n212[22(n1)2(n1)Cn1]

=n2[22n3122n2Cn1]

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