ΣnFib(n+2)x^(n+2) is F(x)−x−1 because it's an infinite series of powers of x, except since it's x^(n+2) then x^1 (x) and x^0 (1) never appear, so you need to su

ΣnFib(n+2)x^(n+2) is F(x)−x−1 because it's an infinite series of powers of x, except since it's x^(n+2) then x^1 (x) and x^0 (1) never appear, so you need to subtract them from F(x) which is ΣnFib(n)x^n. I hope that's clear and explains the rest.