Given:

Total terms after expansion = 2n-1+1=2n

Middle term = 2n/2 = nth term

So two required middle terms are : nth & (n+1)th term

k= (n-1) & n for both terms respectively.

(1 + x)^2n-1

Coefficient of nth term;

=^2n-1C_n-1

Coefficient of (n+1)th term ;

= ^2n-1C_n

Sum of coefficients = ^2n-1C_n-1 + ^2n-1C_n

= ^2n-1+1C_n

=²ⁿC_n