In this section, we give a simpler closed-form combinatorial representation for Fibonacci
numbers. To do so, we first give a closed-form representation for the number of vertices
|V (Fh)| of Fh (the Fibonacci tree of height h). One of the most powerful methods of solving
equations is called Guess-and-Check - We can use any method to figure out a solution to an
equation and then determine whether it is right by substituting it in the equation and checking
the equation is solved by the guessed solution. This method is particularly powerful when used
with differential equations, recurrence equations and simultaneous equations - Such a method
is employed in the following lemma to calculate the number of vertices in a particular level of
Fh and thereafter we sum the number of vertices over the levels to get |V (Fh)|.