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1、授课人：授课人： 09数本数本2陈祥英陈祥英Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.复习回顾1.等差数列的概念等差数列的概念2.等差数列的通项公式等差数列的通项公式an=a1+(n-1
2、)dan-an-1=d (nN*且且 n2)Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.2.3.1 等差数列的前等差数列的前n n项和项和 ？Evaluation only.Created
3、 with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.共共5050个个101101于是所求的和是于是所求的和是高斯求和的本质是什么？这种求和方法有没有缺点？Evaluation only.Created with Aspose.Slides f
4、or .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. 泰泰姬姬陵陵座座落落于于印印度度古古都都阿阿格格，是是十十七七世世纪纪莫莫卧卧儿儿帝帝国国皇皇帝帝沙沙杰杰罕罕为为纪纪念念其其爱爱妃妃所所建建，她她宏宏伟伟壮壮观观，纯纯白白大大理理石石砌砌建建而而成成的的主主体体建建筑筑叫叫人人
5、心心醉醉神神迷迷，成成为为世世界界七七大大奇奇迹迹之之一一。陵陵寝寝以以宝宝石石镶镶饰饰，图图案案之细致令人叫绝。之细致令人叫绝。 传传说说陵陵寝寝中中有有一一个个三三角角形形图图案案，以以相相同同大大小小的的圆圆宝宝石石镶镶饰饰而而成成，共共有有100100层层（见见左左图图），奢奢靡靡之之程程度，可见一斑。度，可见一斑。你你知知道道这这个个图图案案一一共共花花了了多多少少宝宝石吗？石吗？猜猜看有多少宝石？探究：探究：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright
6、 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.问题问题1：图案中，第：图案中，第1层到第层到第21层一共有层一共有多少颗宝石？多少颗宝石？ 这这是是求求奇奇数数个个项项的的和和的的问问题题，能能不不能能直直接接用用高高斯斯的的办办法呢求和呢？法呢求和呢？Evaluation only.Created with Aspose.Slides for .NET 3.5
7、Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. 问题问题1:图案中，第图案中，第1层到第层到第21层一层一共有多少颗宝石？共有多少颗宝石？ Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Co
8、pyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.212120191获得算法：123Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Create
9、d with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. ( (倒序相加）倒序相加）问题问题2:求求1到到n这这n个正整数之和。个正整数之和。 即Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .N
10、ET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.等差数列等差数列 的前的前 项和公式：项和公式：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-201
11、1 Aspose Pty Ltd.（1 1） ；例例1.1.求和：求和：（2 2） （结果用（结果用 表示）表示）（3 3） （结果用（结果用 表示）表示）Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pt
12、y Ltd.解例解例1：（1）由公式得：）由公式得：（2）原式可写成：）原式可写成：（3）同理有）同理有Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.例题例题2： 已知一个等差数列已知一个等
13、差数列 前前10项的和是项的和是310，前，前20项的和是项的和是1220. 由这些条件能确定这个等差数列的前由这些条件能确定这个等差数列的前n项和公式吗？项和公式吗？解：解：由题意可知由题意可知将它们代入公式将它们代入公式得到：得到：解这个关于解这个关于与与d的方程组，得到：的方程组，得到：所以：所以：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspo
14、se.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.巩固练习：巩固练习：(2004.全国全国)等差数列等差数列 的前的前n项和记为项和记为 已知已知（1）求通项）求通项（2）令）令,求求nEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.S
15、lides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.再如：再如：“今有女子善织布，逐日所今有女子善织布，逐日所织的布以同数递增，初日织五尺，计织的布以同数递增，初日织五尺，计织三十日，共织九匹三丈，问日增几织三十日，共织九匹三丈，问日增几何？何？” 南北朝时，张丘建始创等差数列求和解法。他在南北朝时，张丘建始创等差数列求和解法。他在张丘建算经里给出了几个等差数列问题。张丘建算经里给出了几个等差数列问题。例如：例如：“今有女子不善织布，逐日所织之布以同今有女子不善织布，逐日所织之布以同数递减，初
16、日织五尺，末一日织一尺，计织三十日，数递减，初日织五尺，末一日织一尺，计织三十日，问共织几何？问共织几何？” 原书的解法是：“并初、末日织布数，半之，余以乘织讫日数，即得。” 思考与余味思考与余味: :Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyri
17、ght 2004-2011 Aspose Pty Ltd.2学习了等差数列的前学习了等差数列的前n项和公式：项和公式：与与1经历了等差数列前经历了等差数列前n n项和公式推倒的过程，项和公式推倒的过程，将高斯算法进行推广。将高斯算法进行推广。学了什么学了什么?课堂小结：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET
18、 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.作业：作业：（1）必做题：）必做题：1题和题和2题题（2）选做题：）选做题：B组的组的3题和题和4题题Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.谢谢观看谢谢观看Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.
