畢業(yè)論文設(shè)計(jì)-《斐波那契數(shù)列》

畢業(yè)論文設(shè)計(jì)-《斐波那契數(shù)列》斐波那契數(shù)列摘要關(guān)鍵詞斐波那契數(shù)列；定義和性質(zhì)；應(yīng)用Geometry-thearithmeticmeaninequalityanditsapplicationinalgebraAbstractGeometry-thearithmeticaverageofinequalityisveryimportantinequality,Themostwidelyusedinmodernanalyticalmathematics,Manyoftheconclusionsprovedtobeusingthisinequalityonthebasisof,Cleveruseofthisinequalitycanmakemanyoftheproblemsisabeautifulsolution,Broughtalotofconvenienceforourresearchwork.Theproofofthisinequalityandweareinterestedin.WiththeinequalitycontinuestobeprovenandbeusedtoprovetheotherconclusionsLeadtotheuseofinequalitygreatlyadvanee.Geometry-thearithmeticaverageoftheinequalityintheextremevalue,theconditionalextremumseekingsomeiterativeserieslimit,seriesconvergeneeandinequalityderivationofalargenumberofwidelyused,Applythisinequalitycanbemanyunexpectedresults,Italsoresultsoftheuseanddevelopmentofavarietyoftransformation.Onthegeometry-thearithmeticmeaninequalityresearchandextension,ourproblem-solvingideaswillbetodevelopmathematicalthinkingwillbeacorrespondingincreasein,whichisofpracticalsignificaneetoexploresomeofthesubstantiveissues.KeywordsGeometry-thearithmeticaverageofinequality;ElementaryProof;Theuseofinequality1引言研究背景和意義公元1202年，意大利數(shù)學(xué)家列昂納多?斐波那契〔LeonardoFibonacci,生于公元1170年，卒于1240年，籍貫大概是比薩〕撰寫(xiě)了一本?珠算原理?，他被人稱(chēng)作“比薩的列昂納多〞，他是第一個(gè)研究印度和阿拉伯?dāng)?shù)學(xué)的歐洲人，書(shū)中提到了一種數(shù)列：1、1、2。3、5、&13、21這個(gè)數(shù)列從第三項(xiàng)開(kāi)始，每一項(xiàng)都等于前兩項(xiàng)之和。這個(gè)數(shù)列引起了很多數(shù)學(xué)家的關(guān)注，后來(lái)人們稱(chēng)其為斐波那契數(shù)列。書(shū)中的兔子問(wèn)題，也被譽(yù)為經(jīng)典的數(shù)列模型。繼兔子問(wèn)題以后，斐波那契數(shù)列得到了蓬勃的開(kāi)展。至今為止，斐波那契數(shù)列不光在數(shù)學(xué)領(lǐng)域，在物理，化學(xué)甚至金融領(lǐng)域等各個(gè)領(lǐng)域都有了廣泛的應(yīng)用。研究現(xiàn)狀本文的主要工作及內(nèi)容2斐波那契數(shù)列的定義和性質(zhì)斐波那契數(shù)列的定義定義：一個(gè)數(shù)列，前兩項(xiàng)都為1,從第三項(xiàng)起，每一項(xiàng)都是前兩項(xiàng)之和，那么這個(gè)數(shù)列稱(chēng)為斐波那契數(shù)列，又稱(chēng)黃金分割數(shù)列。表達(dá)式Fo=1,Fi=1,Fn=Fn-i+Fn-2〔nN〕通項(xiàng)公式〔又叫“比內(nèi)公式〞，是用無(wú)理數(shù)表示有理數(shù)的一個(gè)范例〕比擬有趣的是：一個(gè)完全是自然數(shù)的數(shù)列，通項(xiàng)公式竟然是用無(wú)理數(shù)表示的斐波那契數(shù)列通項(xiàng)公式的證明下面是其通