Let be a positive integer

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

n

be a positive integer. For the binomial expansion of

(1+x)^n

answer the following questions. (i) Define what is meant by “the sum of the coefficients” in the expansion of

(1+x)^n

. (ii) Show, without actually expanding

(1+x)^n

, that the sum of the coefficients is

2^n

. (iii) For

n=8

, find separately the sum of the coefficients of the terms that contain an even power of

x

and the sum of the coefficients of the terms that contain an odd power of

x

. Give reasons for each answer.