I'm trying to prove that
( 1 + x + x^2 + x^3 + ... + x^2k) ( 1 - x + x^2 - x^3 + ... + x^2k)
= 1 + x^2 + x^4 + ... + x^4k, where k is a positive integer and x is not equal to -1, 1.
This question was posted in the section on Geometric Progressions.
I don't know how to begin with this... is x^2k the last term? What does it mean, is it a power of 2?? For example x raised to some power of 2??
Do I use the summation formula S_n = a ( 1 - r^n) / (1 -r)??
Help will be appreciated.