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AP EAMCET202318 May 2023Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x^3 in the expansion of (1-x)^ 3 / 2 , (|x| < 1) is

Options

  1. A- 3 16
  2. B1 16
  3. C1 8
  4. D3 16

Correct answer

B. 1 16

Step-by-step solution

The expansion of (1-x)^ 3 / 2 is aligned & (1-x)^ 3 / 2 =1+ 3 2 (-x)+ ( 3 2 ) ( 3 2 -1 )(x)^2 2 ! & + 3 2 ( 3 2 -1 ) ( 3 2 -2 ) 3 ! (-x)^3+ & =1- 3 2 x+ 3 8 x^2+ 1 16 x^3+ & Coefficient of x^3= 1 16 aligned

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