Question

Fibonacci series explanation

Answer 1

You start off with 0,1 and then every number after is the sum of the previous two numbers 0,1, 1 (sum of 1 and 0) then 2 (sum of 1 and 1), 3,5,8,13....

Answer 2

We can define the Fibonacci series recursively. Let F(n) be the nth term of the sequence. Then F(n + 2) = F(n + 1) + F(n), F(0) = 0, F(1) = 1.
This recurrence relationship is a difference equation with initial conditions and can be solved using techniques from the calculus of finite differences. The Fibonacci sequence has several interesting properties related to the golden ratio.