Fibonacci Series

The Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding ones. It starts with 0 and 1, and each subsequent number is the sum of the two previous numbers.

Here's an example of the Fibonacci series:

10, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The Fibonacci series can be implemented using recursion. The recursive definition of the Fibonacci series is as follows:

• Base case: If n is 0 or 1, return n.
• Recursive case: Return the sum of the two previous Fibonacci numbers.

Let's take a look at an example implementation of the Fibonacci series in Java:

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In this example, the fibonacci function takes an integer n as input and returns the n-th Fibonacci number. The function uses recursion to calculate the Fibonacci number. The base case is when n is 0 or 1, in which case the function returns n. The recursive case is when n is greater than 1. In this case, the function calculates the Fibonacci number by summing the two previous Fibonacci numbers (fibonacci(n - 1) and fibonacci(n - 2)). This recursive call continues until the base case is reached, resulting in the desired Fibonacci number.

Try running the example code to see the 6th Fibonacci number being calculated and printed to the console.

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public class Main {

  public static int fibonacci(int n) {

    // Base case: If n is 0 or 1, return n

    if (n == 0 || n == 1) {

      return n;

    }

​

    // Recursive case: Return the sum of the two previous Fibonacci numbers

    return fibonacci(n - 1) + fibonacci(n - 2);

  }

​

  public static void main(String[] args) {

    // Example call to fibonacci for n = 6

    int result = fibonacci(6);

    System.out.println(result);

  }

}