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COMEDK2018MathematicsBinomial Theorem

If c₀, c₁, c₂, , c_ n are binomial coefficients of order n , then the value of c₁ 2 + c₂ 4 + c₃ 6 +

Options

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

Correct answer

B. 2^ n -1 n+1

Step-by-step solution

We have, c₁ x+c₃ x³+c₅ x⁵+ = 1 2 (1+x)^ n -(1-x)^ n ₀¹ (c₁ x+c₃ x³+c₅ x⁵+ ) d x= 1 2 ₀¹(1+x)^ n -(1-x)^ n d x c₁ 2 + c₃ 4 + c₅ 6 + = 2^ n -1 n+1 _ 5 ( 1 4 + 1 4.2 + 1 4 ( 1 2 )²+ )

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