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Let $C_{r} =^{15} C_{r}, 0 \leq r \leq 15 .$ Sum of the series $S = \sum_{r = 1}^{15} r (\frac{C_{r}}{C_{r - 1}})$ is

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Correct option is D

CrCr−1=15!r!(15−r)!×(r−1)!(16−r)!15!=16−rr⇒S=∑r=115 rCrCr−1=∑r=115 (16−r)=12(15)(16)=120

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Let Cr=15Cr,0≤r≤15. Sum of the series S=∑r=115 rCrCr−1 is

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Let $C_{r} =^{15} C_{r}, 0 \leq r \leq 15 .$ Sum of the series $S = \sum_{r = 1}^{15} r (\frac{C_{r}}{C_{r - 1}})$ is