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Question

The value of C01.3C12.3+C23.3C34.3++(1)nCn(n+1).3 is


A

3n+1

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B

n+13

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C

13(n+1)

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D

None of these

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Solution

The correct option is C

13(n+1)


(1+x)n=C0+C1x+C2x2++Cnxn
On integrating from - 1 to 0
C0C12+C23+(1)nCnn+1=1n+1
Hence required = 13(n+1)


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