Euler-Binet Formula/Proof 3

Proof
This follows as a direct application of the first Binet form:


 * $U_n = m U_{n - 1} + U_{n - 2}$

where:

has the closed-form solution:
 * $U_n = \dfrac {\alpha^n - \beta^n} {\Delta}$

where:

where $m = 1$.

It is also known as Binet's Formula.