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Question

Prove that C0+C1+C2+.....Cn=2n

A
2n
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B
2n1
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C
2n+1
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D
None of the above.
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Solution

The correct option is A 2n
(1+x)n=nC0+nC1x++nCnxn

Let x=1

C0+C1.1+C2.12++Cn.1n=(1+1)n=2n

C0+C1+C2.1++Cn=(1+1)n=2n

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