Fibonacci series is a number series named after the mathematician called Fibonacci. Beginning with 0 and 1, every new number in the Fibonacci series represents the 2 numbers before it. For instance, starting with 0 and 1, the first 5 numbers of the Fibonacci sequence will be 0,1, 1, 2, and 3. At the outset, calculating the Fibonacci series seems simple, but when the number of digits becomes bigger, the calculation becomes complex. Here we are going to see how to create a Fibonacci series in the C++ language.
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Significance of Fibonacci numbers
Fibonacci numbers are often used as technical indicators as they are a reliable mathematical sequence. This sequence was developed by an Italian mathematician named Fibonacci in the 13th century. The first few terms of the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 etc.
This sequence can be broken down into ratios that can be used for complex analysis such as stock market predictions. The main significance of the Fibonacci sequence is its golden ratio, 1.618. This means that, in a Fibonacci sequence, any number is roughly 1.618 times the previous number except the first few numbers. Every number is also 0.618 times the number to its right, again except for the first few numbers. The golden ratio is vital in calculating several theories in science.
How to calculate the terms of the Fibonacci series
Assume that f(n) is the nth term of the Fibonacci series.
Then the nth term is f(n).
f(0) = 0;
f(1) = 1;
and so on. And the series will be as follows:
1(1 + 0),
2 (1+1),
3 (1+2),
5 (2+3),
8 (3+5),
13 (5+8),
21 (8+13),
And so on.
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Logic to generate the Fibonacci Series
Given below are the steps to generate the terms of the Fibonacci Series:
- Initialize the first term with the value of 0.
- Initialize the second term with the value of 1.
- Add the first and the second terms.
- Store the above period in a third term.
- Print the third term.
- Assign the second term to the first term.
- Assign the third term to the second term.
- Repeat steps 3 to 7 until the Fibonacci series is calculated for a given number.
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