Find the middle term (terms) in the expansion of
(i) `((x)/(a) - (a)/(x))^(10)` (ii) `(3x - (x^(3))/(6))^(9)`

Explanation

The number of terms in the expansion of `(3x - (x^(3))/(6))^(9)` is ltbRgt 10 (even). So , there are two middle terms
`i.e. ((9 +1)/(2)) "th and "((9 + 3)/(2))` th terms . They are given by ` T_(5) `
and `T_(6)`
` therefore T_(5) = T_(4 + 1) = ""^(9)C_(4) (3x)^(5) (-(x^(3))/(6))^(4)`
` = (9* 8* 7* 6)/(1*2*3*4). 3^(3) x^(5) (x^(12))/(6^(4)) = (189)/(8) x^(17)`
and ` T_(6) = T_(5 +1) = ""^(9)C_(5) (3x)^(4) ((x^(3))/(6))^(5)`
` = ""^(9)C_(4) * 3^(4) *x^(4) * (x^(15))/(6^(5))`
` = - (9*8*7*6)/(1*2*3*4) 3^(4) (x^(19))/(6^(5)) = - (21)/(16) x^(19)` .