FIBONACCI Numbers Formulae

You have reached the web pages of RAJESH RAM (  This page contains some of the results that I have found   on Fibonacci Numbers.   Click here for a Text Version of this page. Click here for my mathematics home page.  Click here for a mathematics directory from

Other Pages : PELL Numbers FormulaeSums of PowersFIBONACCI Numbers FormulaeTRIANGLE Numbers that are Perfect Squares, Sums of Cubes, Sums of Powers - Ramanujan and his Number 1729

A brief introduction to Fibonacci Numbers : 1,1,2,3,5,8,13,21,34,55,89,....... which is given by

fibointro.gif (1414 bytes)

For more information on Fibonacci Numbers please see Dr. Ron Knott's excellent site at

The following is a list of Fibonacci Formulae that I have found. 

Formula involving e, i and PI :

FKeiPi.gif (2206 bytes)

which is the same as

wpe1.gif (1960 bytes)



Please note that I do know that formuala F1 is already known.  The only reason I am still keeping it here is because I feel my list would be incomplete without its presence here.  I discovered F1 without ever knowing that it had already been found long ago.  I discovered the others after F1.  
Fk1.gif (1447 bytes) F1
fk2.gif (1889 bytes) F2
fk3.gif (1800 bytes) F3
fk4.gif (1937 bytes) F4
fk5.gif (1614 bytes) F5
fk6.gif (1692 bytes) F6
fk7.gif (2190 bytes) F7
fk8.gif (2190 bytes) F8
fk9.gif (2237 bytes) F9
fk10.gif (1994 bytes) F10
fk11.gif (1978 bytes) F11
fk12.gif (2531 bytes) F12
fk13.gif (2111 bytes) F13
fk14.gif (2276 bytes) F14
fk15.gif (2470 bytes) F15
fk16.gif (2488 bytes) F16