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COMEDK2024MathematicsBinomial Theorem

Middle term of the expansion (x^2+ 1 x^2 +2 )^n is

Options

  1. A^ 2 n C_n
  2. B2 n n+1
  3. C^ 4 n C_n
  4. D4 n n+1

Correct answer

A. ^ 2 n C_n

Step-by-step solution

We have, (x^2+ 1 x^2 +2 )^n= (x+ 1 x )^ 2 n Coefficient of middle term of (x+y)^n , if n is even = ^n C_ n / 2 Coefficient of middle term of (x+ 1 x )^ 2 n = 2 n 2 n 2 = ^ 2 n C_n

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