The famous Fibonacci sequence is a sequence of numbers, which starts
from two ones, and then each consecutive term is a sum of the previous
two. It describes many things in nature. In a symbolic form we can
write: \(F_0 = 1, F_1 = 1, F_n = F_{n-1} +
F_{n-2}\).
Show that \[F_0+F_1+ F_2 + \dots + F_n =
F_{n+2}-1\]