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BITSAT2013MathematicsBinomial TheoremActual

If C ₀, C ₁, C ₂, . C _ n denote the binomial coefficientsin the expansion of (1+ x )^ n , then the value of C ₀+ ( C ₀+ C ₁ )+ ( C ₀+ C ₁+ C ₂ )+ + (C₀+C₁+ . .+C_ n-1 )

Options

  1. An 2^ n -1
  2. Bn 2^ n
  3. C(n-1) 2^ n-1
  4. D(n-1) 2^ n

Correct answer

A. n 2^ n -1

Step-by-step solution

aligned & C ₀+ ( C ₀+ C ₁ )+ ( C ₀+ C ₁+ C ₂ )+ &+ ( C ₀+ C ₁+ . C _ n -1 ) &= n C ₀+( n -1) C ₁+( n -2) C ₂+ C _ n -1 &= C ₁+2 C ₂+3 C ₃+4 C ₄ n C _ n = n .2^ n -1 aligned

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