## Fibonacci Series:

### what is fibonacci series:

In mathematic, the

**Fibonacci numbers**are the numbers in the following integer sequence, called the**Fibonacci sequence**, and characterized by the fact that every number after the first two is the sum of the two preceding ones:The sequence

*F*of Fibonacci numbers is defined by the recurrence relation:

_{n}#### Iterative Solution:

#### #include <stdio.h>

####

int main()

{

int a=0,b=1,c=1,n,i;

scanf("%d",&n);

if(n==0)

printf("%d",a);

else if(n==1)

printf("%d",b);

else

{

for(i=2;i<=n;i++)

{

c=a+b;

a=b;

b=c;

}

printf("The %d term is %d",n,c);

}

return 0;

}

#### Input :4

#### Output:

#### The 4 term is 3

#### Recursive Solution:

####
#include<stdio.h>

int fib(int n)

{

if (n <= 1)

return n;

return fib(n-1) + fib(n-2);

}

####
int main ()

{

int n = 4;

printf(The %d term is %d",n,fib(n));

return 0;

}

#### Input :4

#### Output:

#### The 4 term is 3

#### Recurssive tree for fibonacci series

The recursive solution is simple the recursion continues until the input parameter value is 0 or 1.Then it will return 0 or 1 based on input and it will be

added to recursion call location so you can clearly see in recursion tree the sum at the child node is added at current parent node and this process continues until the summing reaches to the root of the recursion tree and it will be the output of our input.

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