If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$
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For a quick test, substitute a small value like $n = 1$. This gives $a_1 = \frac{1}{1} + \frac{1}{1} = 2$ and $b_1 = \frac{0}{1} + \frac{1}{1} = 1$. The ratio is $\frac{1}{2}$, which matches $\frac{n}{2}$.