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NDA2013MathematicsBinomial TheoremActual

What is _ r=0 ^n C(n, r) equal to?

Options

  1. A2^n-1
  2. Bn
  3. Cn!
  4. D2^n

Correct answer

D. 2^n

Step-by-step solution

aligned &(1+x)^n= ^n C ₀+ ^n C ₁ x+ ^n C ₂ x^2+ + ^n C _n x^n & for x=1 &(2)^n= ^n C ₀+ ^n C ₁+ ^n C ₂+ ^n C ₃+ + ^n C _n & _ r=0 ^n C (n, r)=(2)^n . aligned

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