Middle term in binomial expression:

There are two types

(a) When n is even

Clearly in that type we have only one middle term namely T_{n/2 + 1}. Therefore middle term in the expansion of (a + x)ⁿ will be ⁿC_n/2 a^n/2x^n/2  term.

(b) When n is odd

Obviously in that type we have two middle terms defined as .  That denotes the middle terms in the expansion of (a +x)ⁿ are .

 Illustration: Calculate the middle term in the expansion of . 

Solution: There will be two middle terms as n = 9 is an odd number. The middle terms may be  terms.         

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