Let be a positive integer greater than 1

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

Problem

Let

n

be a positive integer greater than 1. Consider the binomial expansion of

(1+x)^n

. (i) Prove that the sum of the coefficients of the terms containing even powers of

x

equals the sum of the coefficients of the terms containing odd powers of

x

. (ii) Deduce that each of these sums is

2^{n-1}

. (iii) Using the result of part (ii), calculate the common value of these two sums when

n=7

. No credit will be given for brute-force expansion.