The value of $\binom{n}{1} + 2\binom{n}{2} + 3\binom{n}{3} + \cdots + n\binom{n}{n}$ equals:
Step-by-Step Solution
Key Concept: Use the identity $r\binom{n}{r} = n\binom{n-1}{r-1}$ to rewrite each term of the sum, factor out the common $n$, and recognise the remaining sum as the total of all binomial coefficients of $(1 + x)^{n-1}$.
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Correct Answer: (2)