If n is an odd natural number, then n∑r=0(−1)rnCr equal to
A
0
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B
1n
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C
n2n
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D
12n
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Solution
The correct option is D0 n∑r=0(−1)rnCr =1−1nC1+1nC2−1nC3+...−1nCn ...(since n is odd, the ending term will have a negative coefficient) =(1−1nCn)+(1nCn−1−1nC1)+(1nC2−1nCn−2)... =0 ...(Using property of binomial coefficient)