Looks like a reciprocal binomial

Algebra Level 3

Suppose we denote \(\displaystyle a_n \) as the value of \(\displaystyle \sum_{r=0}^n \dfrac1{^n C_r } \), express \(\displaystyle \sum_{r=0}^n \dfrac r{^n C_r} \) in terms of \(n\) and/or \(a_n\).

Clarification:

\(^n C_r \) denote the binomial coefficient, \( \dbinom{n}{r} = \dfrac{n!}{r!(n-r)!} \).

Practice for Bitsat here.
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