InterviewSolution
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InterviewSolution
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The coefficient of `x^(4)` in the expansion of `(1-ax-x^(2))/(e^(x))` isA. `(-1)r/(r!){-r^(2)+r(a+1)+1}`B. `(-1)r/(r!){-r^(2)-r(a+1)+1}`C. `(-1)r/(r!){-r^(2)-r(a+1)+1}`D. none of these |
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Answer» Answer: We have `(1-ax-x^(2))/(e^(x))=e^(-x)-axe^(x)-x^(2)e^(-x)` `therefore` coefficient of `x^(r ) in (1-ax-x^(2))/(e^(x))` =coefficient of `x^(r ) in e^(-x)-axe^(-x)-x^(2)e^(-x)` =coefficient of `x^(r ) "in" e^(-x)-a xx "coefficient" of x^(r-1) "in" e^(-x)-"coefficient of" x^(r-2) "in" e^(x)` `=(-1)^(r)/(r!)-a(-1)^(r-1)/(r-1)!-(-1)^(r-2)/(r-2)!` `=(-1)^(r)/(r!){1+ar-r(r-1)}` |
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