fibonacci series.

yeah .....
here goes d progrm
#include<iostream.h>
#include <conio.h>
void main()
{
int fo,f1,f,n;
fo=0;
f1=1;
cout<<"fibbonacci series
";
cout<<"
"<<fo<<"
"<<f1;
for(i=3;i<=n;i++)
{
f=fo+f1;
cout<<:
"<<f;
fo=f1;
f1=f2;
}
}
u i'll get d fibbonacci series

let me state first that it is a general way to find nth term of a linear recurrence relation.

suppose Fn=a* F(n-1)+ b* F(n-2).
here a=b=1.

replace F(n) by xⁿ. i'm not explaining why. those who are interested may check a topic called GENERATING FUNCTION.

you get a equation x²-a*x-b=0. [here x²-x-1=0]

get the two roots. let they be α,β.

then general term is F(n)= k₁* (α)ⁿ + k₂ * (β)ⁿ .

value of k₁ and k₂ are to be found by putting n=1 and n=2.

i forgot to mention above is only valid iff α≠β. for α=β,
F(n)=(k1+k2* n)* (α)ⁿ.

http://targetiit.com/iit-jee-forum/posts/poser-test-your-mind-1656.html

all this seems so historical , almost black and white .....