Write a Java program to generate the Fibonacci series using recursion.

This program calculates and prints the Fibonacci series up to a given number of terms using a recursive approach. Below is an explanation of how the program works:

class Main {
    public static void main(String[] args) {
        int terms = 5;  // The number of terms in the Fibonacci series
        System.out.print("Fibonacci series up to " + terms + " terms: ");
        
        // Loop to print Fibonacci numbers from 0 to terms-1
        for (int i = 0; i < terms; i++) {
            System.out.print(fiboSeries(i) + " ");  // Print each Fibonacci number followed by a space
        }
    }

    // Method to calculate Fibonacci number at position n
    public static int fiboSeries(int n) {
        if (n == 0) {
            return 0;  // The 0th Fibonacci number is 0
        } else if (n == 1) {
            return 1;  // The 1st Fibonacci number is 1
        } else {
            return fiboSeries(n - 1) + fiboSeries(n - 2);  // Recursive calculation
        }
    }
}

Output:

Fibonacci series up to 5 terms: 0 1 1 2 3 

Key Concepts

Fibonacci Series:
A sequence where each number is the sum of the two preceding ones.
Starts with 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, …

Recursive Approach:
The fiboSeries method calculates the Fibonacci number at position n using:
Base cases: fiboSeries(0) = 0 and fiboSeries(1) = 1
Recursive case: fiboSeries(n) = fiboSeries(n-1) + fiboSeries(n-2)

Main Method:
Specifies the number of terms (terms).
Uses a loop to compute and print Fibonacci numbers for all positions from 0 to terms-1.
Example Execution for terms = 5
Call Stack for fiboSeries(4):

The series generated: 0, 1, 1, 2, 3

Advantages of Recursive Approach
Simple and elegant for smaller inputs.
Closely mimics the mathematical definition of Fibonacci numbers.

Performance Consideration
Inefficient for Large Inputs:
Each call generates two more recursive calls, leading to an exponential growth of calls.
Example: fiboSeries(5) computes fiboSeries(3) twice and fiboSeries(2) three times.