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1、浅谈数列求和的若干方法摘要纵观近几年来的高考试题,数列一直被列为重要考察内容之一,数列求和问题更是数列中的一个重要组成部分,常常在压轴题中出现。随着数学的发展,数列求和出现了新题型。对于这些既非等差又非等比的特殊数列,学生常感到无从下手求和。对这部分内容有畏难情绪,以至没有学好此内容。高中数学必修五(人民教育出版社)对数列的求和只是介绍了等差数列和等比数列求和公式的推导和应用,而特殊数列求和所用的倒序相加法、裂项相消法、错位相减法等这些常规的、重要的方法在课本中都没有相关的例题介绍,由于课本没有这些方法的详细介绍,教师在教学过程屮往往是直接讲结论后让学生模仿着
2、去应用,学生不清楚这个结论逐步形成的过程,就体会不到蕴涵在其中的思想方法,只懂得机械的模仿,在做题时,如果题廿稍有变化,他们的思维就转不过弯來,或者时间长了他们就容易遗忘。木文就根据特殊数列的不同特点和结构对特殊数列的求和进行分类,并通过一些具体的例子归纳出特殊数列求和的方法。关键词:数列;数列求和;等差数列;等比数列;前项和;倒序相加法;错位相减法;裂项相消法;分组求和法;数学归纳法。AbstractThroughoutrecentyears,theCollegeEntranceExamination,thenumberofcolumnshasbeenlis
3、tedasoneoftheimportantstudycontent,theproblemisthenumberofcolumnsinthesummationoftheseriesisanimportantpart,andoftenappearinthetitleofthefinale.Thedevelopmentofmathematics,thenumberofcolumnssummingtheemergenceofnewkindsofquestions.Fortheseareneitherarithmeticandgeometricnon-specific
4、sequence,studentsoftenfeelunabletostartthesummation.Thispartofthecontentsoffearofhardship,andevendidnotlearnthiscontent.Highschoolmathematicscompulsoryfive(People'sEducationPress)isjustthesumofthenumberofcolumnsintroducesArithmeticandgeometricsequenceisderivedandappliedsummationform
5、ula,andspecialseriessummationmethodusedinreverseadding,splitentrydestructivemethod,subtraction,etc.Theseconventionaldislocationandimportantmethodintextbooksarenotrelevantexample,duetothetextbooksdonotdetailthesemethods,theteachersintheteachingprocessisoftendirectlyspeaktotheconclusi
6、onallowstudentstoimitatetheapplication^studentsthisprocessgraduallyclearconclusion,youcannotunderstandtheimplicationofthinkinginwhichonlyknowsthemechanicalimitation,indoingthat,ifthetitleisslightlychangedtheirthinkingontheturn,butturnto,oralongtimetheyareeasilyforgotten.Inthispaper,
7、dependingonthecharacteristicsandstructuresofspecialcolumnssummingseriesofspecialclassification,andthroughsomeconcreteexamplessummarizethespecialseriessummationmethod.Keywords:thenumberofcolumns;seriessummation;arithmeticsequence;geometricsequence;firstnitems;descendingadditivemethod
8、;dislocationsubtrac