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Question

C12+C34+C56+...

A
2n+11n+1
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B
2n1n+1
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C
2nn+1
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D
1n+1
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Solution

The correct option is A 2n1n+1
(1=x)n=nC0+nC1X....
Integrate
(1+x)n+1n+1=nC0x+nC1x22...
First with limits 0 to 1
2m+1m+11m+1=nC0+nC12...(1)
then -1 to 0
(1)m+1m+1=0=0
nC0(1)+nC1x22
1n+1=nC0nC12.........(2)
Subtracting (1) & (2)
2n1n+1=nC12+nC34

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