InterviewSolution
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InterviewSolution
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The coefficient of `x^(-17)` in the expansion of `(x^4-1/x^3)^(15)` is |
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Answer» Given expansion is `(x^(4) - (1)/(x^(3)))^(15)` Let the term `T_(r + 1)` constains the coefficient of `(1)/(x^(17))` i.e., `x^(-17)` `:. T_(r + 1) = .^(15)C_(r) (x^(4))^(15 - r) (-(1)/(x^(3)))^(r)` `= .^(15)C_(r) x^(60 - 4xr) (-1)^(r) x^(-3r)` `.^(15)C_(r) x^(60 - 7r) (-1)^(r)` For the coefficient `x^(-17)`, `60 - 7r = - 17` `rArr 7 r = 77 rArr r = 11` `rArr T_(11 + 1) = .^(15)C_(11) x^(60 - 77) (-1)^(11)` `:.` Coefficient of `x^(-17) = (-15 xx 14 xx 13 xx 12 xx 11 !)/(11! xx 4 xx 3 xx 2 xx 1)` `= - 15 xx 7 xx 13 - 1365` |
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