1/(1-z) = (1+z)(1+z^2)(1+z^4)(1+z^8)...
Both sides as formal power series work out to 1 + z + z^2 + z^3 + ..., where all the coefficients are 1. This is an analytic version of the fact that every positive integer can be written in exactly one way as a sum of distinct powers of two, i. e. that binary expansions are unique.
