Find the middle term in the expansion of `((2x)/3-3/(2x))^(20)`

Explanation

`n=20` (Even number)

Therefore, the middle term is the `(frac{n}{2}+1)` th term, i.e, the 11th term.

Now,

`T_{11}=T_{10+1}`

`=\ ^{20} C_{10}(frac{2}{3} x)^{20-10}(frac{3}{2 x})^{10} `

`=\ ^{20} C_{10} frac{2^{10}}{3^{10}} times frac{3^{10}}{2^{10}} x^{10-10} `

`=\ ^{20} C_{10}`