Find the middle term in the expansion of (x – 1/x)2n+1

where, n = (2n + 1) is an (odd number)

So the middle terms are \( \dfrac{(n+1)}{2}\)

= \(\dfrac{ (2n+1+1)}{2}\)

=\(\dfrac{ (2n+2)}{2}\) = (n + 1) and

\( \dfrac{(n+1)}{2} + 1\)

=\(\dfrac{ (2n+1+1)}{2 + 1}\)

= (n + 1 + 1) = (n + 2)

The terms are (n + 1)^th and (n + 2)^th.

Now,

T_n = T_n+1

And,

T_n+2 = T_n+1+1

Hence, the middle term is (-1)ⁿ.²ⁿ⁺¹C_n x and (-1)ⁿ⁺¹.²ⁿ⁺¹C_n (\( \dfrac{1}{x}\)).