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Question

The value of nr=1r nCr nCr1 is

A
n(n+1)2
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B
(n+1)22
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C
n22
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D
n(n1)2
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Solution

The correct option is A n(n+1)2
nr=1r nCr nCr1=nr=1r(nr+1)r=nr=1(nr+1)=nr=1(n+1)nr=1r=(n+1)nr=11nr=1r=(n+1)nn(n+1)2=n(n+1)2

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