The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It typically starts with 0 and 1, and each subsequent number is the sum of the previous two. This sequence appears in many natural phenomena and has applications in various fields of mathematics and science.

To calculate Fibonacci numbers, start with 0 and 1, then generate each subsequent number by adding the two previous numbers in the sequence. This process continues indefinitely, creating an ever-growing sequence of numbers.

The formula for calculating the nth Fibonacci number is:

\[ F_n = F_{n-1} + F_{n-2} \]

Where F_{n} is the nth Fibonacci number, with initial conditions F_{0} = 0 and F_{1} = 1.

- Start with F
_{0}= 0 and F_{1}= 1 - For each subsequent number n, calculate F
_{n}= F_{n-1}+ F_{n-2} - Continue this process for as many numbers as needed in the sequence

Let's calculate the first 8 Fibonacci numbers:

- F
_{0}= 0 - F
_{1}= 1 - F
_{2}= F_{1}+ F_{0}= 1 + 0 = 1 - F
_{3}= F_{2}+ F_{1}= 1 + 1 = 2 - F
_{4}= F_{3}+ F_{2}= 2 + 1 = 3 - F
_{5}= F_{4}+ F_{3}= 3 + 2 = 5 - F
_{6}= F_{5}+ F_{4}= 5 + 3 = 8 - F
_{7}= F_{6}+ F_{5}= 8 + 5 = 13

Therefore, the first 8 Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13

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