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NDA2015MathematicsBinomial TheoremActual

Consider the expansion of (1+x)^ 2 n+1 The sum of the coefficients of all the terms in the expansion is

Options

  1. A2^ 2 n -1
  2. B4^ n -1
  3. C2 4^ n
  4. DNone of the above

Correct answer

C. 2 4^ n

Step-by-step solution

Sum of all coefficient aligned & = ^ (2 n +1) C ₀+ ^ (2 n +1) C ₁+ . .+ ^ (2 n +1) C _ 2 n +1 & =(1+1)^ 2 n +1 & =2^ (2 n +1) & =2.2^ 2 n & =2.4^ n aligned

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