Let n be a positive integer greater than 1.
Consider the binomial expansion of (1+x)n.
a. (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.
b. (ii) Deduce that each of these sums is 2n−1.
c. (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.