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AP EAMCET2006MathematicsBinomial Theorem

The coefficient of x^n in 1-2 x e^x is :

Options

  1. A(1+2 n) n !
  2. B(-1)^n (1+2 n) n !
  3. C(-1)^n (1-2 n) n !
  4. D(-1)^n (1+4 n) n !

Correct answer

C. (-1)^n (1-2 n) n !

Step-by-step solution

1-2 x e^x =(1-2 x) e^ -x =(1-2 x) (1-x+ x^2 2 ! - x^3 3 ! + . .+(-1)^n x^n n ! + ) Coefficient of x^n in 1-2 x e^x = (-1)^n n ! - 2(-1)^n (n-1) ! =(-1)^n (1-2 n) n !

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