InterviewSolution
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InterviewSolution
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Find the coefficient of `x^(15)` in the expansion of `(x - x^(2))^(10)` |
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Answer» Given expansion is `(x - x^(2))_(10)` Let the term `T_(r + 1)` is the general term `:. T_(r + 1) = .^(10)C_(r) x^(10 - r) (-x^(2))^(r)` `= (-1)^(r) . .^(10)C_(r). X^(10 - r) . X^(2r)` `= (-1)^(r) .^(10)C_(r) x^(10 + r)` For the coefficient of `x^(15)`, `10 + r = 15 rArr r = 5` `T_(5 + 1) = (-1)^(5) .^(10)C_(5) x^(15)` `:.` Coefficient of `x^(15) = - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5 xx 4 xx 3 xx 2 xx 1 xx 5!)` `= - 3 xx 2 xx 7 xx 6 = -252` |
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