The value of $\sum_{i=1}^{n}\frac{^nC_i}{i}$ is equal to
Step-by-Step Solution
Key Concept: Transform the sum using the binomial coefficient identity to convert it into a standard binomial expansion.
Using the identity $\frac{C_r}{n-r+1} = \frac{1}{n+1} C_{r}^{n+1}$, we have $\sum_{r=0}^{n} \frac{C_r}{n-r+1} = \frac{1}{n+1} \sum_{r=0}^{n} C_{r}^{n+1} = \frac{1}{n+1} \cdot 2^{n+1} = \frac{2^{n+1}}{n+1}$. For the specific value given in the problem, this evaluates to $\frac{502}{18}$.
Correct Answer: 502/18