数列求和导学案.doc

四川省金堂中学 2015学年高一数学必修五导学案 编制人：杨 聪 审核：高中数学组数列求和导学案【学习目标】1能熟练地应用等差数列、等比数列前项和公式解决有关数列求和问题；2掌握非等差数列、等比数列求和的几种常用方法.【学习重、难点】1重点是倒序相加法、裂项相消法、错位相减法；2难点是能根据通项选择合适的方法求和.课前自学案【自主学习】-勇敢试知识回顾1数列的前项和的定义：_；2若数列是等差数列则公式：；公式：_；想一想：在上述公式的推导中采用了什么数学方法？试试再一次书写推导过程：3.若数列是等比数列则公式：；公式：_；想一想：在上述公式的推导中采用了什么数学方法？试试再一次书写推导过程：自主探究试试完成下列求和：1、_；2、_； 3、_；4、_；5、_； 课堂探究案合作学习、交流展示-大胆讲问题1、谈谈你解自主探究1、2两小题的思路？问题2、观察自主探究第3题中的前后对称项，看看有什么关系？问题3、我们知道通分运算：，也就是说可以裂项为 .你能尝试仿照上述过程写出一些裂项运算的等式吗？问题4、等比数列的前n项和公式推导过程对解自主探究第5题有什么启示作用 ？引导、点拨、归纳- 一起来1、 倒序相加求和法：例1.已知函数.（1）证明：；（2）求的值.归纳领悟： 2、裂项相消求和法：例2.求数列的前n项和.归纳领悟： 3、错位相减求和法：例3.求数列的前n项和.归纳领悟：【课堂练学】- 一定行1.等差数列的前四项之和为26，最后四项之和为110，所有项之和为187，则该等差数列共有多少项？2.求数列的前项和.3.求和：【整合提升】- 谈收获数列求和的几种方法：心得体会：课后练学案1.求和：2.求和：3.求数列的前项和.4.若函数对任意都有。（1），数列是等差数列吗？若是，请证明你的结论；（2）求数列的的前项和。课外探究学习教育储蓄是一种零存整取定期储蓄存款，它享受整存整取利率，利息免税教育储蓄的对象是在校小学四年级（含四年级）以上的学生假设零存整取3年期教育储蓄的月利率为（1）欲在3年后一次支取本息合计2万元，每月大约存入多少元？（2）零存整取3年期教育储蓄每月至多存入多少元？此时3年后本息合计约为多少？（精确到1元）？说明：教育储蓄可选择1年、3年、6年这三种存期，起存金额50元，存款总额不超过2万元。自学要求：课前认真限时完成,规范书写. 自学要求：课前认真思考、积极自主探究.探究要求：积极交流，互评质疑，踊跃发言，流利表达，全面展示自我.学法指导：感知模型，听分析，归纳通性通法，看规范格式、书写.想一想：例1第一小问中结论的本质是什么？想一想：该数列的通项可以裂项吗？如果可以，用到的运算方法是什么？观察第2小题中通项的分母让你联想到什么？第3小题问中如果去掉后面括号内的限制又怎么解决呢？culture and entertainment venues, fitness centers, has a good ecological environment, job security measures), these requirements are very straightforward, specific standards, also has a clear direction, more easily by a superior examination. Poverty assessment is to look at the per capita net income of the poor end of 2015 standards is . . Yuan, higher standards is poverty. Superior acceptance to entrust a third party institution from HouseImplementation. After acceptance, also through spot checks, visits, telephone surveys looking activities. This means that our achievements have been recognized by the poor for poverty alleviation through acceptance, which we put forward higher requirements for poverty eradication. Therefore, the County Office for poverty alleviation to evaluation efforts in this regard. To implement the grid management model, integrating poverty alleviation into grid management, and make a heart activity combined package of leading cadres implement monitoring systems for poverty alleviation, each poor households identified a package cost. In this regard, you can design a form, indicating the poor basic causes, current income, poverty, support measures, implementation of support measures, through helping income, annual revenue. From now on, protection officers working households, household-by-place. When the examination, which the poor dont have time to get out of poverty, and holding people accountable. Third, on environmental protection in construction of ecological civilization is the focus on one of the six battle this year. Xian Wei proposed to build green mountains and beautiful, happy and harmonious new . . Target, which is the basis of environmental protection. Do well environmental protection work, we keep the side of the mountains, nor to the masses to create a suitable for residential and business suitable for swimming and raising living and working environment. Last year, we got good grades the environmental work, atmospheric index ranked 4th in the city to obtain eco-compensationaccording to project needs, in accordance with the channel, use the same, and use principle, the implementation of project planning, funding and manpower arrangements, avoiding duplication of inputs and waste of resources, effective integration of poverty relief funds . Here to remind everyone that bundle integration-related funds, aims to concentrate financial resources for big undertakings. Authorities do not think that has less autonomy, pursuing the deregulation of work. This year on the amount of funds on fighting for the departments concerned to increase over the previous year . and . respectively. In this regard, the financial Department to dispatch in a timely manner, analyses relevant departments strive for. (E) to implement the poverty assessment responsibilities. Of village-level evaluation is very clear, that is, five-ten (five-way path, p