**Fibonacci Series**start with a Zero and the next element is one then first we print 0 and 1. Now add two previous elements and print the next element as 0+1=1. repeat the process again and again until you get your answer.

0+1=1

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13

8+13=21

13+21=34. . . .

## Fibonacci Series in C++

```
#include <iostream>
using namespace std;
int main()
{
int a = 0, b = 1, i, n, c;
cout << "Enter The Number \n\n"; //Enter the number of terms
cin >> n;
cout << "\nFibonacci Series Is \n\n"; //Fibonacci Series Is given below
cout << a << " " << b << " ";
for (i = 0; i < n; i++)
{
c = a + b; //here adding two previous value
cout << c << " ";
a = b; //swap the value
b = c; //here first two value results are stored in 'b' } //Loop end.
cout << "\n";
return 0;
}
```

### Fibonacci Series

Fibonacci Series in C++: In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and are characterized by the fact that every number after the first two is the sum of the two preceding ones.

Often, especially in modern usage, the sequence is extended by one more initial term.

The Fibonacci numbers occur in the sums of "shallow" diagonals in Pascal's triangle seen in the given picture

**Fibonacci Series:**1 ,1 ,2 ,3 ,5 ,8 ,13 ,21 ,34.Often, especially in modern usage, the sequence is extended by one more initial term.

**Fibonacci Series:**0 ,1 ,1 ,2 ,3 ,5 ,8 ,13 ,21 ,34.The Fibonacci numbers occur in the sums of "shallow" diagonals in Pascal's triangle seen in the given picture

Important Fact about the Fibonacci Series: 'The 'Golden Ratio' or Phi' of any two consequent numbers of the sequence in the Fibonacci Series in C++ is 1.618 or 1.6 (approx) Except for starting 4 terms.

3 / 2 = 1.500

5 / 3 = 1.667

8 / 5 = 1.600

13 / 8 = 1.625

21 / 13 = 1.615

34 / 21 = 1.619

55 / 34 = 1.617

89 / 55 = 1.618

144 / 89 = 1.618

233 / 144 = 1.618

377 / 233 = 1.618

610 / 377 = 1.618

987 / 610 = 1.618

1597 / 987 = 1.618

2584 / 1597 = 1.618

4181 / 2584 = 1.618

6765 / 4181 = 1.618

**Example:**The first 21 Fibonacci numbers Fn for n = 0, 1, 2, …, 20 are given below.**Fibonacci Series:**0 ,1 ,1 ,2 ,3 ,5 ,8 ,13 ,21 ,34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765.3 / 2 = 1.500

5 / 3 = 1.667

8 / 5 = 1.600

13 / 8 = 1.625

21 / 13 = 1.615

34 / 21 = 1.619

55 / 34 = 1.617

89 / 55 = 1.618

144 / 89 = 1.618

233 / 144 = 1.618

377 / 233 = 1.618

610 / 377 = 1.618

987 / 610 = 1.618

1597 / 987 = 1.618

2584 / 1597 = 1.618

4181 / 2584 = 1.618

6765 / 4181 = 1.618

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