For r=0,1,...,10, let Ar, Br, and Cr denote, respctively, the coeffici – InterviewSolution

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1.	For r=0,1,...,10, let Ar, Br, and Cr denote, respctively, the coefficient of xr in the expansions of (1+x)10, (1+x)20 and (1+x)30. Then ∑10r=1Ar(B10Br−C10Ar)is equal to
Answer» For $r = 0, 1, . . ., 10$ , let $A_{r}, B_{r},$ and $C_{r}$ denote, respctively, the coefficient of $x^{r}$ in the expansions of $(1 + x)^{10}, (1 + x)^{20}$ and $(1 + x)^{30}$ . Then $\sum_{r = 1}^{10} A_{r} (B_{10} B_{r} - C_{10} A_{r})$ is equal to

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