InterviewSolution
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InterviewSolution
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The coefficient of `x^(n)` in the expansion of `(a+bx+cx^(2))/(e^(x))` isA. `(-1)^(n)/(n!){cn^(2)-(b+c)(n+a}`B. `(-1)^(n)/(n!){cn^(2)+(b+c)(n+a}`C. `(-1)^(n)/(n!){cn^(2)+(b+c)(n-a}`D. none of these |
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Answer» Answer: We have `(a+bx+cx^(2))/(e^(x))=ae^(-x)+bxe^(-x)+cx^(2)e^(-x)` =coefficient of `x^(n) "in" (a+bx+cx^(2)+ex)` =coefficient of `x^(n) in (ae^(-x)+bxe^(-x)+cx^(2)e^(-x)` `=a("coeff of" x^(n)) in e^(-x))+b("coeff of" x^(n-1)) in e^(-x)+("coeff of" x^(n)-2) in e^(-x))` `=a(-1)^(n)/(n!)-bn(-1)^(n)/(n!)+c(-1)^(n)n(n-1)/(n!)` `=(-1)^(n)/(n!){a-bn+cn(n-1)}` |
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