dla n>1

0, 1, 1, 2, 3, 5, 8,
13, 21, ...

1

,

0

1

0





F

F

1

2









n

n

n

F

F

F

Function
rfib(n:LongInt):LongInt;
begin
if n=0 then rfib:=0 else
if n=1 then rfib:=1 else
rfib:=rfib(n-2)+rfib(n-
1);
end;

i

x

y

f

0

0

1

2

0

1

0+1=1

3

1

1

1+1=2

4

1

2

1+2=3

5

2

3

2+3=5

6

3

5

3+5=8

7

5

8

5+8=13

Function fib(n:LongInt):LongInt;
var x,y,f,i:LongInt;
begin
if n=0 then f:=0 else
if n=1 then f:=1 else
begin
x:=0; y:=0; f:=1;
for i:=2 to n do
begin
x:=y; y:=f; f:=x+y;
end;
end;
fib:=f;
end;

Program w Pascalu

[F

n+1

, F

n

]=[1, 0]•

n

0

1

1

1





































 













 



n

n

n

F

2

5

1

2

5

1

5

1

 



















n

n

n





1

5

1















5

n



Wzór
Bineta

1

1

1

1

2

1

1

3

3

1

1

4

6

4

1

1

5

10

10

5

1

1

6

15

20

15

6

1

1

7

21

35

35

21

7

1

1

8

28

56

70

56

28

8

1

1

1

2

3

5

8

13

21

34

Trójkąt
Pascala





















 



2

/

0

1

n

k

n

k

k

n

F





























2

/

)

1

(

0

1

1

2

5

2

1

n

k

n

n

n

k

n

F











1

lim

n

n

n

F

F

 



















1

1

1

1

1

n

n

n

n

F

F



 

n

n

n

n

F

F

F

1

2

1

1













1

2

1

1

2

4



















n

n

n

n

n

F

F

F

F

F

n

k

n

k

F

F

k

n

2

0



















n

k

k

n

k

F

F

k

n

3

0

2

















