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If binomial coefficients of three consecutive terms of (1+x)² are in H P , then the maximum value of n is

Options

  1. A1
  2. B2
  3. C0
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Let the coefficients of rth, (r+1) th, and (r + 2) th terms be in HP. Then, 2 n r = 1 n r-1 + 1 n r +1 array l 2= ^ n C _ r ^ n C _ r -1 = ^ n C _ r ^ n C _ r +1 2= n - r +1 r + r +1 n - r n ²-4 nr +4 r ²+ n =0 ( n -2 r )²+ n =0 array which is not possible for any value for n .

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