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AP EAMCET2006MathematicsBinomial Theorem

If |x| < 1 and y=x- x^2 2 + x^3 3 - x^4 4 + , then x is equal to :

Options

  1. Ay+ y^2 2 + y^3 3 +
  2. By- y^2 2 + y^3 3 - y^4 4 +
  3. Cy+ y^2 2 ! + y^3 3 ! +
  4. Dy- y^2 2 ! + y^3 3 ! - y^4 4 ! +

Correct answer

C. y+ y^2 2 ! + y^3 3 ! +

Step-by-step solution

y=x- x^2 2 + x^3 3 - x^4 4 + y= (1+x) 1+x=e^y 1+x=1+y+ y^2 2 ! + x=y+ y^2 2 ! + y^3 3 ! +

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