InterviewSolution
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InterviewSolution
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Show that the coefficient of the middle term in the expansion of `(1+x)^(2n)`is equal to the sum of the coefficients of two middle terms in the expansion of `(1+x)^(2n-1)`.A. A+B=CB. B+C=AC. C+A= BD. A+B +C = 0 |
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Answer» Correct Answer - b Clearly, `(n+1)^(th)` term is the middle term in the expansion of `(1 + x)^(2n)` and its coefficients is `""^(2n)C_(n)` i.e. A = `""^(2n)C_(n)` In the expansion of `(1 +x)^(2n-1), n^(th) and (n +1)^(th)` terms are middle terms and their coefficient are `""^(2n)C_(n-1) and ""^(2n-1)C_(n)` respectively i.e. B `""^(2n-1)C_(n-1) and C = ""^(2n)C_(n)`, We have, `""^(2n-1)C_(n-1)+""^(2n-1)C_(n) = ""^((2n-1)+1)C_(n)[because ""^(n)C_(r-1) +""^(n)C_(r) = ""^(n+1)C_(r)]` `therefore B + C = A` |
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