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Manipal MET2017MathematicsBinomial Theorem

The coefficient of x in the expansion of (1+x+x^2+x^3 )⁻³ is

Options

  1. A6
  2. B9
  3. C5
  4. D-3

Correct answer

D. -3

Step-by-step solution

aligned & (1+x+x^2+x^3 )⁻³= [ (x^4-1 ) x-1 ]⁻³ = & (x^4-1 )⁻³(x-1)^3 = & (-1)⁻³ (1-x^4 )⁻³(x-1)^3 = & (-1) (1+3 x^4+ ) (x^3-3 x^2+3 x-1 ) aligned Coefficient of x in (1+x+x^2+x^3 )⁻³ is -3 .

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