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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

|x| < 1 , the coefficient of x^3 in the expansion of (1+x+x^2 ) in ascending powers of x , is

Options

  1. A2 3
  2. B4 3
  3. C- 2 3
  4. D- 4 3

Correct answer

C. - 2 3

Step-by-step solution

We have, (1+x+x^2 )= (1-x^3 ) (1-x) aligned & = (1-x^3 )- (1-x) & =- [x^3+ x^6 2 + x^9 3 + ]+ [x+ x^2 2 + x^3 3 + ] & Coefficient of x^3=-1+ 1 3 =- 2 3 aligned

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