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BITSAT2016MathematicsBinomial TheoremActual

If _ r=0 ^ n r+2 r+1 ^ n C_ r = 2⁸-1 6 , then n=

Options

  1. A8
  2. B4
  3. C6
  4. D5

Correct answer

D. 5

Step-by-step solution

_ r=0 ^ n r+2 r+1 n r = 2⁸-1 6 aligned & _ r=0 ^ n [1+ 1 r+1 ] n r = 2⁸-1 6 & 2^ n + _ r=0 ^ n 1 n+1 n+1 r+1 = 2⁸-1 6 2^ n +& 2^ n+1 -1 n+1 = 2⁸-1 6 2^ n (n+3)-1 n+1 = 2⁸-1 6 & 2^ n (n+1+2)-1 n+1 = 2⁵(6+2)-1 6 aligned Comparing we get n +1=6 n =5

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