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KCET2024MathematicsBinomial Theorem

In the expansion of (1+x)^n C₁ C₀ +2 C₂ C₁ +3 C₃ 2 + +n C_n C_ n-1 is equal to

Options

  1. An(n+1) 2
  2. Bn 2
  3. Cn+1 2
  4. D3 n(n+1)

Correct answer

A. n(n+1) 2

Step-by-step solution

C₁ C₀ +2 C₂ C₁ +3 C₃ C₂ + n C_n C_ n-1 = n 1 +2 n(n-1) 1 2 n +3 n(n-1)(n-2) 3 2 1 n(n-1) n + +n 1 n =n+(n-1)+(n-2) +1= n= n(n+1) 2

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