Find the middle term in the expansion of : `(2x-(x^2)/4)^9`

Explanation

Given expansion term is `(2x− x^2 /4​ )^9`

`n=9= odd`

middle term `=( 9+1 )/2 th +(( 9+3​ )/2) th`

`=5^ (th ) or 6^(th)` term

`T_5​ =T_(4+1)​ =\ ^9 C_4​ (2x)^5 (( −x^2 ​ )/4 )^4 `

= `(9!)/(4!5!)​ 2^5 ×x^5 (−1)^4 × (x^8)/(4^4) `
​
= `(9×8×7×6×5!​ )/(4×3×2×5!)× (2^5x^13)/(2^5) .1`

`​T_5​ = (63)/(4)​ x^13`
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