Fibonacci Series

🌀 What is the Fibonacci Series?

The Fibonacci sequence is a mathematical wonder where each number is the sum of the two preceding ones. It usually starts with 0 and 1. It’s not just a math concept—it appears everywhere in nature, from the spirals of shells to the arrangement of leaves on a stem!

The sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Mathematically, it is defined by the formula:

Fn​=Fn−1​+Fn−2​

🛠️ Step-by-Step Code Explanation

Instead of a table, here is the breakdown grouped by "Logic Blocks":

1. Setup & Input

• import java.util.Scanner; Imports the utility needed to read what the user types.
• Scanner in = new Scanner(System.in); Creates a "listener" object named in to capture keyboard input.
• int num = in.nextInt(); Stores the user's chosen limit into the variable num.

2. The Starting Seeds

• int n1 = 0, n2 = 1, nn = 0; We initialize our variables. n1 and n2 are the first two numbers of the series. nn (next number) is a placeholder for the calculation.

3. The Logic Loop

• for(int i = 1; i <= num; ++i) This loop acts as a counter. It will run exactly as many times as the value of num.
• System.out.print(n1 + ", "); Prints the current number in the sequence.

4. The "Sliding Window" Calculation

• nn = n1 + n2; Adds the current two numbers together to find the next one.
• n1 = n2; The Shift: The old second number now becomes the first number.
• n2 = nn; The Update: The newly calculated number (nn) now becomes the second number.

Written by : @Varnit_Baiswar
import java.util.Scanner;
class Fibonacci_Series
{
  public static void main()
  {
    Scanner in = new Scanner(System.in);
    System.out.println("Enter a Number: ");
    int num = in.nextInt();
    int n1 = 0, n2 = 1, nn = 0;
    System.out.println("Fibonacci Series Upto " + num + " :");
    for(int i = 1;i <= num; ++i)
    {
      System.out.print(n1+", ");
      nn = n1+n2;
      n1 = n2;
      n2 = nn;
    }
    System.out.println();
  } 
}