(i) (3x – x3/6)9
Now, we have,
(3x – x3/6)9 where, n = 9 (odd number)
Therefore the middle terms are ((n + 1)/2) = ((9 + 1)/2) = 10/2 = 5 and
((n + 1)/2 + 1) = ((9 + 1)/2 + 1) = (10/2 + 1) = (5 + 1) = 6
The terms are 5th and 6th.
Then,
T5 = T4+1
Thus, the middle term are 189/8 x17 and -21/16 x19.
(ii) (2x2 – 1/x)7
Now we have,
(2x2 – 1/x)7 where, n = 7 (odd number)
Therefore the middle terms are ((n + 1)/2) = ((7 + 1)/2) = 8/2 = 4 and
((n + 1)/2 + 1) = ((7 + 1)/2 + 1) = (8/2 + 1) = (4 + 1) = 5
The terms are 4th and 5th.
Then,
Thus, the middle term are -560x5 and 280x2.
(iii) (3x – 2/x2)15
We have,
(3x – 2/x2)15 where, n = 15 (odd number)
Therefore the middle terms are ((n + 1)/2) = ((15 + 1)/2) = 16/2 = 8 and
((n + 1)/2 + 1) = ((15 + 1)/2 + 1) = (16/2 + 1) = (8 + 1) = 9
The terms are 8th and 9th.
Now,
Thus, the middle term are (-6435×38×27)/x6 and (6435×37×28)/x9.
(iv) (x4 – 1/x3)11
Here, we have,
(x4 – 1/x3)11
where, n = 11 (odd number)
Therefore the middle terms are ((n + 1)/2) = ((11 + 1)/2) = 12/2 = 6 and
((n + 1)/2 + 1) = ((11 + 1)/2 + 1) = (12/2 + 1) = (6 + 1) = 7
The terms are 6th and 7th.
Now,
Thus, the middle term are -462x9 and 462x2.