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BITSAT2018MathematicsBinomial TheoremActual

The coefficient of x - n in 1 + x n 1 + 1 x n is

Options

  1. A0
  2. B1
  3. C2 n
  4. D2 n

Correct answer

B. 1

Step-by-step solution

1 + x n 1 + 1 x n = 1 + x 1 + 1 x n 1 + x n 1 + 1 x n = 1 + x + 1 x + 1 n 1 + x n 1 + 1 x n = 2 + x + 1 x n 1 + x n 1 + 1 x n = C 0 n 2 + x n · 1 x + C 1 n 2 + x n - 1 · 1 x 1 + … + C n n · 1 x n ∴ Coefficient of x - n = C n n = 1

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