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$If S_{n} = \sum_{i = 0}^{n} \frac{1}{^{n} C_{r}} and t_{n} = \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}} then \frac{t_{n}}{S_{n}} =$

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12n

2n−12

n−1

12n−1

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detailed solution

Correct option is A

tn=∑r=0n r nCr=∑r=0n n−r nCn−r=∑r=0n n−r nCr=n∑r=0n 1 nCr−∑r=0n r nCr=nsn−tn⇒2tn=nsn⇒tnSn=n2

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If Sn=∑i=0n 1 nCr and tn=∑r=0n r nCr then tnSn=

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$If S_{n} = \sum_{i = 0}^{n} \frac{1}{^{n} C_{r}} and t_{n} = \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}} then \frac{t_{n}}{S_{n}} =$