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Question
Find the middle term in the expansion of `(x/y + y/x)^12`
Solution
Here, a = `x/y`, b = `y/x`, n = 12
Now, n is even
∴ `("n" + 2)/2 = (12 + 2)/2` = 7
∴ Middle term is t7, for which r = 6.
We have, tr+1 = nCr an–r .br
∴ t7 = `""^12"C"_6 (x/y)^6.(y/x)^6 = (12!)/(6!6!)`
= `(12 xx 11 xx 10 xx 9 xx 8 xx 7)/(6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 924
∴ Middle term is 924
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