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Question
n∑r=1n−1Cr−1 =
n∑r=1n−1Cr−1 =
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Solution
The correct option is C
n∑r=1n−1Cr−1 = n−1C0 + n−1C1.............n−1Cn−1
It's the sum of the coefficients of the expansion (1+x)n−1. We get the sum of the coefficients when
we put x = 1
⇒ n∑r=1 n−1Cr−1 = (1+1)n−1
= 2n−1
n∑r=1n−1Cr−1 = n−1C0 + n−1C1.............n−1Cn−1
It's the sum of the coefficients of the expansion (1+x)n−1. We get the sum of the coefficients when
we put x = 1
⇒ n∑r=1 n−1Cr−1 = (1+1)n−1
= 2n−1
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