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Manipal MET2010MathematicsBinomial Theorem

The greatest coefficient in the expansion of (1+x)^ 2 n is

Options

  1. A^ 2 n C_n
  2. B2 n n-1
  3. C2 n n-2
  4. DNone of these

Correct answer

A. ^ 2 n C_n

Step-by-step solution

The coefficient of t_ r+1 The coefficient of t_r = ^ 2 n C_r 2 n r-1 = 2 n-r+1 r The coefficient of t_ r+1 The coefficient of t_r , provided 2 n-r+1 r 1 or 2 n+1 2 r or, r 2 n+1 2 or r n+ 1 2 Hence, the greatest coefficient = The coefficient of (n+1) th term = ^ 2 n C_n= (2 n)! (n!)^2

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