If \( \sum_{r=0}^{10}\left(\frac{r}{{ }^{10} C_{r}}\right)=20 \), find the value of \( \sum_{r=0....

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If \( \sum_{r=0}^{10}\left(\frac{r}{{ }^{10} C_{r}}\right)=20 \), find the value of \( \sum_{r=0}^{10}\left(\frac{1}{{ }^{10} C_{r}}\right) \).
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