InterviewSolution
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InterviewSolution
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Given positive integers `r>1,n> 2, n` being even and the coefficient of `(3r)th` term and `(r+ 2)th` term in the expansion of `(1 +x)^(2n)` are equal; find rA. `n = 2r`B. `n = 3r`C. `n = 2r + 1`D. None of these |
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Answer» Given that, `r gt 1, n gt 2` and the coefficients of `(3r) th " and " (r + 2)th` term are equal in the expansion of `(1 + x)^(2n)` Then, `T_(3r) = T_(3r - 1 + 1) = .^(2n)C_(3r - 1) x^(3r - 1)` and `T_(r + 2) = T_(r + 1 + 1) = .^(2n)C_(r + 1) x^(r + 1)` Given, `.^(2n)C_(3r - 1) = .^(2n)C_(r + 1) " " [:. .^(n)C_(x) = .^(n)C_(y) rArr x + y = n]` `rArr 3 r - 1 + r + 1 = 2n` `rArr 4 r = 2n rArr n = (4r)/(2)` `.: n = 2r` |
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