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AP EAMCET202420 May 2024Morning ShiftMathematicsBinomial TheoremActual

If a_n= _ r=0 ^n 1 ^n C_r then _ r=0 ^n r ^n C_r =

Options

  1. A( n -1) a
  2. Bn. an
  3. Cn 2 a_n
  4. Dan ⁺ ₁

Correct answer

C. n 2 a_n

Step-by-step solution

Let b= _ r=0 ^n r ^n C_r ....(i) Replace r by n-rb= _ r=0 ^n n-r ^n C_ n-r ....(ii) Adding (i) and (ii) 2 b= _ r=0 ^n r ^n C_r + _ r=0 ^n n-r ^n C_r b= n 2 _ r=0 ^n 1 ^n C_r b= n 2 a_n

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