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If $C_{0}, C_{1}, C_{2}, \dots, C_{n}$ denote the binomial coefficients in the expansion of $(1 + x)^{n}$ , then
$C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + \dots + \frac{C_{n}}{n + 1} or, \sum_{r = 0}^{n} \frac{C_{r}}{r + 1}$

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2n+1+1n+1

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2n−1n+1

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detailed solution

Correct option is B

We haveC0+C12+C23+…+Cnn+1=∑r=0n Crr+1=∑r=0n 1r+1⋅nCr=∑r=0n 1n+1⋅n+1r+1⋅nCr=1n+1∑r=0n n+1r+1⋅nCr=1n+1∑r=0n n+1Cr+1∵n+1Cr+1=n+1r+1⋅nCr=1n+1 n+1C1+n+1C2+n+1C3+…+n+1Cn+1=1n+1 n+1C0+n+1C1+…+n+1Cn+1− n+1C0=1n+12n+1−1

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2023 | www.infinitylearn.com

If C0,C1,C2,…,Cn denote the binomial coefficients in the expansion of (1+x)n, thenC0+C12+C23+…+Cnn+1 or ,∑r=0n Crr+1

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If $C_{0}, C_{1}, C_{2}, \dots, C_{n}$ denote the binomial coefficients in the expansion of $(1 + x)^{n}$ , then
$C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + \dots + \frac{C_{n}}{n + 1} or, \sum_{r = 0}^{n} \frac{C_{r}}{r + 1}$