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AP EAMCET202315 May 2023Morning ShiftMathematicsBinomial TheoremActual

If C_j stands for ^n C_j , then C ₁ C ₀ + 2 C ₂ C ₁ + 3 C ₃ C ₂ + + n C _ n C _ n -1 =

Options

  1. A_ k =1 ^ n k ^2
  2. B_ k =1 ^ n k 2
  3. C_ k =1 ^ n 2 k
  4. D_ k =1 ^ n k

Correct answer

D. _ k =1 ^ n k

Step-by-step solution

General term for given polinomial r ^n C_r ^n C_ r-1 = r n ! r !(n-r) ! n ! (r-1) !(n-r+1) ! =(n-r+1) Hence aligned & C₁ C₀ + 2 C₂ C₁ + + n C_n C_ n-1 =n+(n-1)+(n-2)+ & =n+(n-1)+(n-2)+ +3+2+1 & = _ k=1 ^n k aligned

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