Question

Find the middle term (terms) in the expansion of `(x/a - a/x)^10`

Answer 1

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`

= 6^th 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