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The value of the sum .^(1000)C_(50) + .^(999)C_(49) +.^(998)C_(48)+"….".^(950)C_(0) is |
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Answer» `.^(1001)C_(50)` `=` coefficient of `x^(950)` in `[(1+x)^(950) + (1+x)^(951) + "....."+(1+x)^(1000)]` `=` coefficientof `x^(950)` in `((1+x)^(950)((1+x)^(51)-1))/((1+x)-1)` `=` coefficient of `x^(950)` in `((1+x)^(1001) - (1+x)^(950))/(x)` `=` coefficient of `x^(951)` in `(1+x)^(1001)` `= .^(1001)C_(1951) = .^(1001)C_(50)` |
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