The Fibonacci series

-

 The Fibonacci series

The Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So, the sequence begins as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

Mathematically, the Fibonacci sequence can be defined recursively as follows:

F(0) = 0 F(1) = 1 F(n) = F(n-1) + F(n-2) (for n > 1)

Here, F(n) represents the nth number in the Fibonacci sequence.

The Fibonacci sequence has a fascinating property where each number in the sequence is the sum of the two preceding numbers. This pattern continues indefinitely, creating an infinite sequence of numbers.

The Fibonacci sequence has numerous applications in various fields, including mathematics, computer science, nature, and finance. It appears in nature in phenomena such as the arrangement of leaves on a stem, the branching of trees, and the spiral patterns found in seashells. In computer science, Fibonacci numbers are used in algorithms, especially for recursive and dynamic programming problems. Additionally, the sequence has connections to the golden ratio and is widely studied in mathematics for its interesting properties and relationships.


COBE:

def fibonacci_series(n): series = [0, 1] # Initialize the series with the first two numbers # Generate the Fibonacci series while len(series) < n: next_number = series[-1] + series[-2] # Calculate the next number series.append(next_number) return series # Example usage n = 10 # Number of Fibonacci numbers to generate result = fibonacci_series(n) print(result)

OUTPUT:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]


Comments

Post a Comment

Popular posts from this blog

ILLUSTRATIVE PROGRAMS IN PYTHON

-
1  Hello, World! Program: print ( "Hello, World!" ) This program simply prints the message "Hello, World!" to the console. 2 Simple Calculator: def add ( a, b ): return a + b def subtract ( a, b ): return a - b def multiply ( a, b ): return a * b def divide ( a, b ): return a / b num1 = float ( input ( "Enter the first number: " )) num2 = float ( input ( "Enter the second number: " )) print ( "Sum:" , add(num1, num2)) print ( "Difference:" , subtract(num1, num2)) print ( "Product:" , multiply(num1, num2)) print ( "Quotient:" , divide(num1, num2)) This program performs basic arithmetic operations (addition, subtraction, multiplication, and division) on two numbers provided by the user.
Read more

Fibonacci Series

-
CODE: def fibonacci(n):     if n <= 0:         return []     elif n == 1:         return [0]     elif n == 2:         return [0, 1]     else:         fib_series = [0, 1]         for i in range(2, n):             fib_series.append(fib_series[i - 1] + fib_series[i - 2])         return fib_series num_terms = int(input("Enter the number of Fibonacci terms: ")) fib_sequence = fibonacci(num_terms) print("Fibonacci Sequence:", fib_sequence)    OUTPUT :                                          Enter the number of Fibonacci terms: 25                                          Fibo...
Read more