2014届高考数学一轮复习名师首选：第6章31《数列的综合应用》学案31数列的综合应用导学目标:1.通过构造等差、等比数列模型，运用数列的公式、性质解决简单的实际问题.2.对数列与其他知识综合性的考查也高于考试说明的要求，另外还要注重数列在生产、生活中的应用(自主梳理1(数列的综合应用数列的综合应用一是指综合运用数列的各种知识和方法求解问题，二是数列与其他数学内容相联系的综合问题(解决此类问题应注意数学思想及方法的运用与体会((1)数列是一种特殊的函数，解数列题要注意运用方程与函数的思想与方法((2)转化与化归思想是解数列有关问题的基本思想方法，复杂的数列问题经常转化为等差、等比数列或常见的特殊数列问题((3)由特殊到一般及由一般到特殊的思想是解决数列问题的重要思想(已知数列的前若干项求通项，由有限的特殊事例推测出一般性的结论，都是利用此法实现的((4)分类讨论思想在数列问题中常会遇到，如等比数列中，经常要对公比进行讨论;由S求a时，要对__________进行分类讨论(nn2(数列的实际应用数列的应用问题是中学数学教学与研究的一个重要内容，解答应用问题的核心是建立数学模型((1)建立数学模型时，应明确是等差数列模型、等比数列模型，还是递推数列模型，是求a还是求S.nn(2)分期付款中的有关规定?在分期付款中，每月的利息均按复利计算;?在分期付款中规定每期所付款额相同;?在分期付款时，商品售价和每期所付款额在贷款全部付清前会随时间的推移而不断增值;?各期付款连同在最后一次付款时所生的利息之和，等于商品售价及从购买时到最后一次付款的利息之和(自我检测1(若S是等差数列{a}的前n项和，且S,S,10，则S的值为________(nn8311a62(在等比数列{a}中，a>a，且a?a,6，a，a,5，则,________.nnn，1711414a163(“嫦娥奔月，举国欢庆”，据科学计算，运载“神六”的“长征二号”系列火箭，在点火第一秒钟通过的路程为2km，以后每秒钟通过的路程都增加2km，在达到离地面240km的高度时，火箭与飞船分离，则这一过程需要的时间大约是________秒(n4(已知数列{a}的通项为a,，则数列{a}的最大项为第________项(nnn2，58n5(设数列{a}，{b}都是正项等比数列，S，T分别为数列{lga}与{lgb}的前n项nnnnnnSnn和，且,，则logba,________.55T2n，1n探究点一等差、等比数列的综合问题例1设{a}是公比大于1的等比数列，S为数列{a}的前n项和(已知S,7，且annn31，3,3a，a，4构成等差数列(23(1)求数列{a}的通项;n(2)令b,lna，n,1,2，„，求数列{b}的前n项和T.n3n，1nnacidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,变式迁移1假设a，a，a，a是一个等差数列，且满足0
4;(3)b>32;(4)bb,256.其中正确命题的个数为n2424________(探究点二数列与方程、函数、不等式的综合问题x，312*,,例2已知函数(),，数列{}满足，?N，fxaa,1，a,fnn1n，13x,a,n(1)求数列{a}的通项公式;n(2)令T,aa,aa，aa,aa，„,aa，求T;n122334452n2n，1nm,20011*(3)令b,(n?2)，b,3，S,b，b，„，b，若S<对一切n?N成立，n1n12nnaa2n,1n求最小正整数m.变式迁移2已知单调递增的等比数列{a}满足:a，a，a,28，且a，2是a，a的n234324等差中项((1)求数列{a}的通项公式;n(2)若b,aa，S,b，b，„，b，对任意正整数n，S，(n，m)a<0恒成立，nnnn12nnn，1log12试求m的取值范围(探究点三数列在实际问题中的应用00元，作为启动资金开店，每月月底例3有一个下岗职工，1月份向银行贷款100获得的利润是该月月初投入资金的20%，每月月底需缴纳所得税为该月月利润的10%，每月的生活费为300元，余款作为资金全部投入下个月的经营，如此继续，问到这年年底这个职工有多少资金,若贷款年利息为25%，问这个职工还清银行贷款后纯收入多少元,变式迁移3假设某市2011年新建住房400万平方米，其中有250万平方米是中低价房，预计在今后的若干年内，该市每年新建住房面积平均比上一年增长8%.另外，每年新建住房中，中低价房的面积均比上一年增加50万平方米(那么，到哪一年底，(1)该市历年所建中低价房的累计面积(以2011年为累计的第一年)将首次不少于4750万平方米,(2)当年建造的中低价房的面积占该年建造住房面积的比例首次大于85%,(参考数据:4561.08?1.36,1.08?1.47,1.08?1.59)1(数列实际应用问题:(1)数学应用问题已成为中学数学教学与研究的一个重要内容，解答数学应用问题的核心是建立数学模型，有关平均增长率、利率(复利)以及等值增减等实际问题，需利用数列知识建立数学模型((2)在试题中常用的数学模型有?构造等差、等比数列的模型，然后再去应用数列的通项公式求解;?通过归纳得到结论，用数列知识求解(acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,2(解决数列综合问题应体会以下思想及方法:(1)数列与函数方程相结合时主要考查函数的思想及函数的性质(多为单调性)((2)数列与不等式结合时需注意放缩((3)数列与解析几何结合时要注意递推思想(课后练习(满分:90分)一、填空题(每小题6分，共48分)，1aa910{}a1(已知等比数列n中，各项都是正数，且a，a2a成等差数列，则的值为13,22a，a78________(2(数列{a}是各项均为正数的等比数列，{b}是等差数列，且a,b，则下列关系正确nn67的是______(填序号)(?a，a?b，b;39410?a，a?b，b;39410?a，a?b，b;39410?a，a与b，b的大小不确定(39410S，S，„，S12n3(有限数列A:a，a，„，a，S为其前n项和，定义为A的“凯森和”，12nnn若有99项的数列，，„，的“凯森和”为1000，则有100项的数列1，，，„，aaaaa129912a的“凯森和”为________(994(有一种细菌和一种病毒，每个细菌在每秒钟末能在杀死一个病毒的同时将自身分裂为2个，现在有一个这样的细菌和100个这样的病毒，问细菌将病毒全部杀死至少需要________秒(2n,是函数,5(已知数列{a}，{b}满足a1，且a，af(x),xbx，2的两个零点，1，1nnnnn则b,________.10222n,2n,1,,,,6(若数列{a}的通项公式a,5,4，数列{a}的最大项为第x项，最小项nnn55,,,,为第y项，则x，y,________.227(函数y,x(x>0)的图象在点(a，a)处的切线与x轴的交点的横坐标为a，其中kkk，1*k?N，a,16，则a，a，a,________.1135*8(把正整数按一定的
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(设a(i，j?N)是位于这个ij三角形数表中从上往下数第i行、从左往右数第j个数，如a,8.若a,2009，则i与j42ij的和为________(124357681012911131517141618202224„„„„„„„„„„„„„„二、解答题(共42分)1x9((14分)已知点(1，)是函数f(x),a(a>0，且a?1)的图象上一点，等比数列{a}n3的前n项和为f(n),c，数列{b}(b>0)的首项为c，且前n项和S满足S,S,S，Snnnnn,1nn,1(n?2)((1)求数列{a}和{b}的通项公式;nn11000(2)若数列{}的前n项和为T，问满足T>的最小正整数n是多少,nnbb2009nn，1acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,10((14分)沿海地区甲公司响应国家开发西部的号召，对西部地区乙企业进行扶持性技术改造(乙企业的经营现状是:每月收入为45万元，但因设备老化，从下月开始需付设备维修费，第一个月为3万元，以后每月递增2万元(甲公司决定投资400万元扶持改造乙企业(据预测，改造后乙企业第一个月收入为16万元，在以后的4个月中，每月收入都比上个月增长50%，而后每个月收入都稳定在第5个月的水平上(若设备改造时间可忽略不计，那么从下个月开始至少经过多少个月，改造后的乙企业的累计总收益多于仍按现状生产所带来的总收益,111((14分)已知函数f(x)满足f(x，y),f(x)?f(y)且f(1),.2*(1)当n?N时，求f(n)的表达式;*(2)设a,n?f(n)，n?N，求证:a，a，a，„，a<2;n123nf,n，1,*(3)设b,(9,n)n?N，S为{b}的前n项和，当S最大时，求n的值(，nnnnf,n,
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八年级地理上册填图题岩土工程勘察试题省略号的作用及举例应急救援安全知识车间5s试题及答案
自主梳理1((4)n,1或n?2自我检测391(222.3.154.85.219课堂活动区例1解题导引1.等差数列与等比数列相结合的综合问题是高考考查的重点，特别是等差、等比数列的通项公式、前n项和公式以及等差中项、等比中项问题是历年命题的热点(2(利用等比数列前n项和公式时注意公比q的取值(同时对两种数列的性质，要熟悉它们的推导过程，利用好性质，可降低题目的思维难度，解题时有时还需利用条件联立方程求解(a，a，a,7123,,解(1)由已知得，解得a,2.,a，3,，,a，4,2,13,3a2,2,设数列{a}的公比为q，由a,2，n222可得a,，a,2q.又S,7，可知，2，2q,7，133qq12即2q,5q，2,0.解得q,2，q,.122由题意得q>1，?q,2，?a,1.1n,1故数列{a}的通项为a,2.nn3n(2)由(1)得a,2，3n，13n?b,lna,ln2,3nln2.n3n，1又b,b,3ln2，?{b}是等差数列，n，1nn?T,b，b，„，bn12nn,b，b,3n,n，1,1n,,?ln2.22acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,n,n，1,3故T,ln2.n2变式迁移14解析设a，a，a，a的公差为d，则a，2d,4，又04，故(2)正确;a,a，d>5，所2322438以b,2a>32，故(3)正确;又a，a,2a,8，所以bb,2a，a,2,256，故(4)正确(442432424例2解题导引这是一道数列、函数、不等式的综合题，利用函数关系式求通项，an观察特点，求出.由再求从而求，最后利用不等式知识求出.TTabSmnnnnn2，31aa2，32nn,,解(1)?a,f,,a，，,n，1n3,a,33nan2?{a}是以为公差的等差数列(n321又a,1，?a,n，.1n33(2)T,aa,aa，aa,aa，„,aan122334452n2n，1,a(a,a)，a(a,a)，„，a(a,a)2134352n2n,12n，154n1,,n，，44,333,,,(a，a，„，a),,?242n33242,,，(2n3n)(911(3)当n?2时，b,,naa2211n,1n,,,,n,n，,33,,33,911,,,,，2,2n,12n，1,91,,又b,3,×1,，?S,b，b，„，b1n12n2,3,911111,,,×1,，,，„，,2,3352n,12n，1,9n19,,,1,,，22,n，1,2n，1m,2001*?S<对一切n?N成立(n29nm,2001即，<22n，19n91,,又?,1,递增，2n，12,2n，1,9nm,200199且?，<.?2n，1222即m?2010.?最小正整数m,2010.变式迁移2解(1)设等比数列{a}的首项为a，公比为q.n1依题意，有2(a，2),a，a，324代入a，a，a,28，得a,8.23433,aq，aq,20，11,,?a，a,20.?242a,aq,8，,,31acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,1,,q,2，q,，,,2,解之，得或,a,2,,1,a,32.,1,q,2，,n,又{a}单调递增，?a,2.?nn,a,2.,11nnn(2),2?log2,,?2，bnn223n?,S,1×2，2×2，3×2，„，n×2.?n234nn，1?,2S,1×2，2×2，3×2，„，(n,1)×2，n×2.?n23nn，1??,?，得S,2，2，2，„，2,n?2nn2,1,2,n，1n，1n，1,,n?2,2,n?2,2.1,2由S，(n，m)a<0，nn，1n，1n，1n，1n，1即2,n?2,2，n?2，m?2<0对任意正整数n恒成立，1n，1n，1?m?2<2,2对任意正整数n，m<,1恒成立(n21?,1>,1，?m?,1，n2即m的取值范围是(,?，,1](例3解依题意，第1个月月余款为,10000(1，a20%),10000×20%×10%,300,11500，1,(×20%×10%,第2个月月底余款为aa1，20%),a300，211依此类推下去，设第n个月月底的余款为a元，n第n，1个月月底的余款为a元，则a,a(1，20%),a×20%×10%,300,1.18an，1n，1nnn,300.下面构造一等比数列(a，xn，1设,1.18，则a，x,1.18a，1.18x，n，1n，xan?a,1.18a，0.18x.?0.18x,,300.n，1n5000a,n，150003?x,,，即,1.18.35000a,n3500050005000?数列{a,}是一个等比数列，公比为1.18，首项a,,11500,,n133329500.3500029500n,1?a,,×1.18，n3350002950011?a,,×1.18，123350002950011?a,，×1.18?62396.6(元)，1233即到年底该职工共有资金62396.6元(纯收入有a,10000(1，25%)12,62396.6,12500,49896.6(元)(变式迁移3解(1)设中低价房的面积形成的数列为{a}，n由题意可知{a}是等差数列，其中a,250，d,50，n1acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,则a,250，(n,1)?50,50n，200，nn,n,1,2S,250n，×50,25n，225n，n22令25n，225n?4750，2即n，9n,190?0，而n是正整数，?n?10.?到2020年底，该市历年所建中低价房的累计面积将首次不少于4750万平方米((2)设新建住房面积形成数列{}，bn由题意可知{}是等比数列，其中,1.08，bb,400，qn1n,1则b,400?(1.08).n由题意可知a>0.85b，nnn,1即50n，200>400?(1.08)?0.85.当n,5时，a<0.85b，55当n,6时，a>0.85b，66?满足上述不等式的最小正整数n为6.?到2016年底，当年建造的中低价房的面积占该年建造住房面积的比例首次大于85%.课后练习区1(3，222.?3.9914(7n1,212n,1解析设至少需要n秒钟，则1，2，2，„，2?100，??100，?n?7.1,25(64an，2nn，1,,，两式相除得，，，„解析依题意有aa2，所以aa2,2，所以aaa，1，1，2135nnnnan45成等比数列，，，，„也成等比数列,1,2,2×2,,aaa，而a，a，所以a32，a1×2246121011,32，又因为a，a,b，所以b,a，a,64.nn，1n1010116(3解析该题是数列知识与函数知识的综合(22224,,2n,2,,n,1，,,n,1，2a,5?,4?,5?,,，n,,,5,,5,555,,，，显然当n,2时，a取得最小值，当n,1时，a取得最大值，此时x,1，y,2，?x，ynn,3.7(21222解析y′,(x)′,2x，则过点(a，a)的切线斜率为2a，则切线方程为y,a,2a(xkkkkk,a)，k2令y,0，得,a,2a(x,a)，kkk11?x,a，即a,a.kk，1k221故{a}是a,16，q,的等比数列，n121n,1即a,16×()，?a，a，a,16，4，1,21.n13528(107解析由数表知，第一行1个奇数，第3行3个奇数，第5行5个奇数，第61行6162×31个奇数，前61行用去1，3，5，„，61,,961个奇数(而2009是第1005个奇数，2故应是第63行第44个数，即i，j,63，44,107.11,,x9(解(1)?f(1),a,，?f(x),.„„„„„„„„„„„„„„„„„„„3,3,(1分)acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,1a,f(1),c,,c，132a,[f(2),c],[f(1),c],,，292a,[f(3),c],[f(2),c],,;32742a81212又数列{a}成等比数列，a,,,,,,c，n1a2333,27?c,1;„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„(2分)a1122n,1,,公比q,,，a,,×n,,a33311,,n*,,2×，n?N;„„„„„„„„„„„„„„„„„„„„„„„„„„(3分),3,?S,S,nn,1()()S,SS，Snn,1nn,1(,S，Sn>2)，„„„„„„„„„„„„„„„„„„„„„„„„„„(4分),1nn又b>0，S>0，?S,S,1.nnnn,1数列{S}构成一个首项为1、公差为1的等差数列，n2S,1，(n,1)×1,n，S,n.„„„„„„„„„„„„„„„„„„„„„„(6nn分)22,,当n?2，b,S,Sn(n,1),2n,1;,1nnn又当n,1时，也适合上式，*?b,2n,1，n?N.„„„„„„„„„„„„„„„„„„„„„„„„„„„(8n分)1111(2)T,，，，„，nbbbbbbbb122334nn，11111,，，，„，1×33×55×7,2n,1,×,2n，1,11111111,,,,,,,1,，,，,，„，2,3,2,35,2,57,11n111,,,,,,1,,.„„„„„„„„„„„„„„„„„(1222,n,12n，1,2,2n，1,2n，1分)n10001000由T,n>，>，得n2n，1200991000?满足T>的最小正整数为112.„„„„„„„„„„„„„„„„„„„(14n2009分)10(解设乙企业仍按现状生产至第n个月所带来的总收益为A(万元)，技术改造后生n产至第n个月所带来的总收益为B(万元)(依题意得nA,45n,[3，5，„，(2n，1)]n2,43n,n，„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„(5分)35，,,，16,12，,,，当n?5时，B,，n3,12acidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,34,,16(n,5),400,81n,594，„„„„„„„„„„„„„„„„„„„„„(10,2,分)2?当n?5时，B,A,n，38n,594，nn22令n，38n,594>0，即(n，19)>955，解得n?12，?至少经过12个月，改造后的乙企业的累计总收益多于仍按现状生产所带来的总收益(„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„(14分)11((1)解令x,n，y,1，1得到f(n，1),f(n)?f(1),2f(n)，„„„„„„„„„„„„„„„„„„„„„„(2分)11?{f(n)}是首项为，公比为的等比数列，221n即f(n),().„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„(52分)(2)证明记S,a，a，a，„，a，n123n1n?a,n?f(n),n?()，„„„„„„„„„„„„„„„„„„„„„„„„„„n2(6分)111123n?S,，2×()，3×()，„，n×()，n2222111111，1234nnS,()，2×()，3×()，„，(n,1)×()，n×()，n222222111112nn，1两式相减得S,，()，„，(),n×()，n2222211n,1n整理得S,2,(),n()<2.n22?a，a，a，„，a<2.„„„„„„„„„„„„„„„„„„„„„„„„(9分)123n1f,n，1,n(3)解?f(n),()，而b,(9,n)n2f,n,1n，1,,n29,,(9,n),.„„„„„„„„„„„„„„„„„„„„„„„„„(1112n,,2分)当n?8时，b>0;当n,9时，b,0;nn当n>9时，b<0，n?n,8或9时，S取到最大值(„„„„„„„„„„„„„„„„„„„„„(14分)nacidity,mL.;M--calibrationofthemolarconcentrationofsodiumhydroxidestandardsolution,moI/L;V--amountofthevolumeofsodiumhydroxidestandardsolution,Ml;M--theweightofthesample,g.Suchaspoormeetstherequirements,takethearithmeticmeanoftheseconddeterminationasaresult.Resultsonedecimal.6,allowingdifferentialanalystsimultaneouslyorinquicksuccessionfortheseconddetermination,theabsolutevalueofthedifferenceoftheresults.Thisvalueshouldbenomorethan1.0.1,definitionsandprinciplesfordeterminationofashinstarches,starchandash:starchsamplesofashtheresidueobtainedafterweight.Originalsampleresidueweightofsampleweightorweightexpressedasapercentageofthedryweightofthesample.Samplesofashat900?hightemperatureuntilashingsample...TheCrucible:determinationofPlatinumorotherconditionsoftheaffectedmaterial,capacityof50mL.Dryer:haseffectivelyadequatedryingagentand-perforatedmetalplateorporcelain.Ashingfurnaces:deviceforcontrollingandregulatingtemperature,offers900incinerationtemperatureof25c.Analyticalbalance.ElectrichotplateorBunsen.3,crucibleofanalysisstepspreparation:Cruciblemustfirstwashwithboilingdilutehydrochloricacid,thenwashwithalotofwaterandthenrinsewithdistilledwater.WashtheCruciblewithinashingfurnace,heatedat900to25?30min,andinthedesiccatortocooltoroomtemperatureandthenweighing,
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