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We often give students a program to write – “To generate a Fibonacci series or Fibonacci Numbers” up to a given no. We need to understand what exactly is Fibonacci series? What is its importance in our lives? Is there any or not?

What is Fibonacci Series?

In the field of mathematics – Fibonacci series or Fibonacci numbers is a series of integers that follows some exact sequence or pattern. Here first two numbers are usually 0 and 1 and every subsequent number is the sum of its previous two numbers. First two numbers can also be 1 and 1. For example:

 0 1 1 2 3 5 8 13 21 34 55 89

Observe, first two numbers are 0 and 1, and every subsequent numbers is sum of previous two numbers.

 0 1 1

next

 0 1 1 2

next

 0 1 1 2 3

next

 0 1 1 2 3 5

and so on…

 0 1 1 2 3 5 8 13 21 34 55 89

From where did Fibonacci numbers or series originated from?

It has its links to Indian Mathematics is relation with Sanskrit prosody, though I have also googled up this information, if you are interested you can find more information on wikipedia.

Assuming :

• A newly born pair of rabbits (one male and one female) are put in a field;
• Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits;
• Rabbits never die and a mating pair always produces one new pair (one male and one female) every month from the second month on.
• The puzzle that Fibonacci posed was: how many pairs will there be in one year?

If you find it bit difficult – you can find the answer on wikipedia.

Fibonacci series is used so many different fields:

Few useful images related to Fibonacci series (courtesy wikipedia): 