Middle term in the expansion of (x²+ 1 x² +2 )^ n is

Step-by-step solution

The given expression is (x² + 1 x² + 2 )^ n . This can be rewritten as (x + 1 x )^ 2n . The number of terms in the expansion of (x + 1 x )^ 2n is 2n + 1 , which is odd. Therefore, there is only one middle term, which is the ( 2n 2 + 1 ) -th term, i.e., the (n+1) -th term. The general term T_ r+1 in the expansion of (a+b)^ m is given by ^ m C_ r a^ m-r b^ r . For the (n+1) -th term, r = n and m = 2n . T_ n+1 = ^ 2n C_ n (x)^ 2n-n ( 1 x )^ n = ^ 2n C_ n x^ n 1 x^ n = ^ 2n C_ n . The value of ^ 2n C_ n is (2n)! n!(2n-