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TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLE CHAPTER 1.TRODUCTION 1.1 Rabbit Problem 2.HISTORICAL BACKGROUND 3.FONACCI SEQUENCE 3.1 Fibonaccinumbers 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 SEQUENCES 5.PROPER.OF GENERALED F~ONACCI SEQUENCE 5.1 Generating function 5.2 Binet's formula 5.3 Limitofthequotientoftwo consecutiveterms 5.4 Catalan's identity 5.5 Cassini's identityor simpson's identity 5.6 docagnes's identity 6.SUM AND DIFFERENCE OF THE SQUARES 0F THE EVEN GENERALIZED FIBONACCI NUMBERS 7.IDENTITIES 0F GEN.FIBONACCI sEQUENCE 8.CONNECTl0N FORMULAS 9.ANOTHER IMPORTANT FORMULAE 10.IDENTITIES FOR/THE COMMON FACTORS 0F GENFIB0Ò»JAC0.AND JACOBsTHAL¡ªLUCAS NUMBERS 11.COMBrNATORIAL FORMULAS INVOLVING GENERALIZED FIBONACCI sEQUENCE l1.1 series ofCombinatorial Identities on(n,k) 11.2 series of Combinatorial Identmes on C(n) 12.CONCLUSION 13.BIBLIOGRAPHY ±à¼­ÊÖ¼Ç