The value of frac{C_1}{C_0} + 2 cdot frac{C_2 | vedclass

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(C) The general term of the series is given by $T_r = r \cdot \frac{^nC_r}{^nC_{r-1}}$.Using the identity $\frac{^nC_r}{^nC_{r-1}} = \frac{n-r+1}{r}$,

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$\frac{n(n+1)}{2}$

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(C) The general term of the series is given by $T_r = r \cdot \frac{^nC_r}{^nC_{r-1}}$.Using the identity $\frac{^nC_r}{^nC_{r-1}} = \frac{n-r+1}{r}$,we substitute this into the expression:$T_r = r \cdot \left( \frac{n-r+1}{r} \right) = n - r + 1$.Now,we sum the terms from $r=1$ to $n$:$S_n = \sum_{r=1}^n (n - r + 1)$.Expanding the summation:$S_n = (n+1) + n + (n-1) + \dots + 1$.This is the sum of the first $n$ natural numbers:$S_n = \frac{n(n+1)}{2}$.

The value of $\frac{C_1}{C_0} + 2 \cdot \frac{C_2}{C_1} + 3 \cdot \frac{C_3}{C_2} + \dots + n \cdot \frac{C_n}{C_{n-1}}$ is equal to

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