Answer the following with reference to the idea of the middle term in a binomial…

MATHEMATICS · Multi-part · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Answer the following with reference to the idea of the middle term in a binomial expansion. (i) For the expansion

(a+b)^n

, state which term(s) are called the middle term(s) when (a)

n

is even, and (b)

n

is odd. (ii) For the expansion

(1+x)^7

, write down the ordinal number(s) (position in the sequence of terms) of the middle term(s). Do not evaluate the terms. (iii) For the expansion

(1+x)^8

, write down the ordinal number of the middle term and express this term symbolically in the form

{n\choose r}a^{n-r}b^{r}

by specifying suitable

n,\;r,\;a,

and

b

. Do not simplify.