What is a Fibonacci series?

Answer 1

The Fibonacci series is a recursively defined sequence of numbers:

x1 = x2 = 1

xn = xn-1 + xn-2

In words: The first two Fibonacci numbers are 1, and each following number is the sum of the two predessors.

1, 1, 2, 3, 5, 8, 13, 21, ...

Note:

There is another definition of the Fibonacci series:

x0 = 0

x1 = 1

xn = xn-1 + xn-2

In this case, the sequence begins with 0:

0, 1, 1, 2, 3, 5, 8, 13, 21, ...
The Fibonacci series is a sequence of numbers, starting with 0 and 1, where each number, starting with the third number, is the sum of the preceding two numbers. The first 11 numbers in this series is 0 1 1 2 3 5 8 13 21 34 55. The ratio of two sequential Fibonacci numbers, as the series approaches infinity, approaches the golden mean, or phi, which has interesting mathematical and other implications.