InterviewSolution
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InterviewSolution
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What is the coefficient of `x^(5)` in the expansion `(1-2x+3x^(2)-4x^(3)+……oo)^(-5)` ?A. `(10!)//(5!)^(2)`B. `5^(-5)`C. `5^(5)`D. `10!//{6!)(4!)}` |
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Answer» Correct Answer - A `1-2x+3x^(2)-4x^(3)+…..` `=(1+x)^(2), so (1-2x+3x^(2)-4x^(3)+….oo)^(-5)` `=((1+x^(-2))=(1+x)^(10) rArr T_(r+1)=""^(10)C_(r)x^®` Putting r=5, coefficient of `x^(5)=""^(10)C_(5)=(10!)/(5!5!)=(10!)/((5!)^(2))` |
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