Chapter 16: Problem 20
For \(\mathrm{r}=0,1, \ldots .10\), let \(\mathrm{A}_{\mathrm{r}}, \mathrm{B}_{\mathrm{r}}\) and \(\mathrm{C}_{\mathrm{r}}\) denote, respectively, the coefficient of \(\mathrm{x}^{\mathrm{r}}\) in the expansions of \((1+x)^{10},(1+x)^{20}\) and \((1+x)^{30}\). Then $$ \sum_{\mathrm{r}=1}^{10} \mathrm{~A}_{\mathrm{r}}\left(\mathrm{B}_{10} \mathrm{~B}_{\mathrm{r}}-\mathrm{C}_{10} \mathrm{~A}_{\mathrm{r}}\right) $$ is equal to A) \(B_{10}-C_{10}\) B) \(\mathrm{A}_{10}\left(\mathrm{~B}_{10}^{2}-\mathrm{C}_{10} \mathrm{~A}_{10}\right)\) C) 0 D) \(C_{10}-B_{10}\)
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