Let be a positive integer.

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

Problem

Let

n

be a positive integer. (i) Expand

(1+x)^{n}+(1-x)^{n}

and simplify the result. (ii) Prove that the simplified expansion obtained in part (i) contains only even powers of

x

. (iii) Obtain a general expression for the coefficient of

x^{2r}

in the expansion from part (i). (iv) For

n=12

, state the number of non-zero terms present in the simplified expansion and write down the middle term(s).