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Question
Answer the following:
Find the middle term (s) in the expansion of `(x - 1/(2y))^10`
Solution
There are 11 terms in the expansion of `(x - 1/(2y))^10`
∴ 6th term is the middle term.
We know that, in the expansion of (a+ b)n,
tr+1 = nCr an-r br
Here a = x, b = `(-1)/(2y)`, n = 10 and for t6, r = 5
∴ middle term = t6 = `""^10"C"_5 (x)^(10 - 5) ((-1)/(2y))^5`
= `(10xx9xx8xx7xx6)/(1xx2xx3xx4xx5)xxx^5xx(-1)/(32y^5)`
= `(-63x^5)/(8y^5)`
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