TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLE CHAPTER 1.TRODUCTION 1.1 Rabbit Problem 2.HISTORICAL BACKGROUND 3.FONACCI SEUENCE 3.1 Fibonaciubers innature 3.2 The Fibonacci sequence even shows up in music 3.3 The Fibonacci spiral 3.4 Construction ofFibonacci spiral 3.5 second Order recursive sequences 4.GENERALED FIBONACCI SEUENCES 5.PROPER.OF GENERALED F~ONACCI SEUENCE 5.1 Generating function 5.2 Binet’s formula 5.3 Limitofthequotientoftwo consecutiveterms 5.4 Catalan’s identity 5.5 Cassini’s identityor sisn’ identity 5.6 docagnes’s identity 6.SUM AND DIFFERENCE OF THE SUARES 0F THE EVEN GENERALZE FIBONACCI NUMBERS 7.ENTITIES 0F GEN.FIBONACCI sEUENCE 8.CONNECTl0N FORMULAS 9.ANOTHER IMPORTANT FORMULAE 10.ENTITIES FOR/THE COMMON FACTORS 0F GENFIB0一JAC0.AND JACOBsTHAL—LUCAS NUMBERS 11.COMBrNATORIAL FORMULAS INVOLVING GENERALZE FIBONACCI sEUENCE l1.1 series ofCombinatorial Identities on(n,k) 11.2 series of Combinatorial Identmes on C(n) 12.CONCLUSION 13.BIBLIOGRAPHY 编辑手记