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Question
Find the middle term (terms) in the expansion of `(x/a - a/x)^10`
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Solution
Given expression is `(x/a - a/x)^10`
Number of terms = 10 + 1 = 11 .....(odd)
∴ Middle term = `((n + 1)/2)^"th"` term
= `(11 + 1)/2`
= `12/2`
= 6th term
General Term `"T"_(r + 1) = ""^n"C"_r x^(n - r) y^r`
⇒ `"T"_(5 + 1) = ""^10"C"_5 (x/a)^(10 - 5) (-a/x)^5`
= `- ""^10"C"_5 x^5/a^5 * a^5/x^5`
= `- ""^10"C"_5`
= `-(10 xx 9 xx 8 xx 7 xx 6)/(5 xx 4 xx 3 xx 2 xx 1)`
= `-9 xx 7 xx 4`
= – 252
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