Question

Find the middle term (terms) in the expansion of `(p/x + x/p)^9`.

Answer 1

Since the power of binomial is odd.

Therefore, we have two middle terms which are 5^th and 6^th terms.

These are given by

T₅ = `""^9"C"_4 (p/x)^5 (x/p)^4`

= `""^9"C"_4 p/x`

= `(126p)/x`

And T₆ = `""^9"C"_5 (p/x)^4 (x/p)^5`

= `""^9"C"_5 x/p`

= `(126x)/p`