InterviewSolution
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InterviewSolution
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If the expansion of `(x - (1)/(x^(2)))^(2n)` contains a term independent of x, then `n` is a multiple of 2. |
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Answer» Given Binomial expansion is `(x - (1)/(x^(2)))^(2n)` Let `T_(r + 1)` term is independent of `x` Then, `T_(r + 1) = .^(2n)C_(r) (x)^(2n - r) (-(1)/(x^(2)))^(r)` `= .^(2n)C_(r) x^(2n - r) (-1)^(r) x^(-2r) = .^(2n)C_(r) x^(2n - 3r) (-1)^(r)` For independent of `x` `2n - 3 r = 0` `:. r = (2n)/(3)` Which is not a integer So, the given expansion is not possible |
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