Aula 12 - Fórmula fechada para a sequência de Fibonacci

Professor: Fabio Henrique Teixeira de Souza Closed Formula for the Fibonacci Sequence In this lesson, we use the method we developed in the previous lesson to find a closed formula for the nth term of the Fibonacci sequence. This method works because the recurrence that defines the Fibonacci sequence is linear and homogeneous of second order, with constant coefficients. The formula found is surprising because it involves nth powers of irrational numbers, but still always yields integers. This formula is also interesting because it leads us to think about the most useful way to express a sequence, since the Fibonacci sequence has a very simple recurrence formula and a complicated closed formula.