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NDA2021MathematicsBinomial TheoremActual

If C₀, C₁, C₂, , C_n are the coefficients in the expansion of (1+x)^n , then what is the value of C₁+C₂+C₃+ +C_n ?

Options

  1. A2^n
  2. B2^n-1
  3. C2^ n-1
  4. D2^n-2

Correct answer

B. 2^n-1

Step-by-step solution

(1+x)^n=C₀+C₁ x+C₂ x^2+C₃ x^3+ .+C_n x^n For, x=1 , aligned & (1+1)^n=C₀+C₁+C₂+C₃+ .+C_n & 2^n=1+C₁+C₂+C₃+ .+C_n aligned ^n C₀= ^n C_n=1 C₁+C₂+C₃+ . .+C_n=2^n-1

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