[数项级数的基本概念及其性质.ppt

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2017-01-08 发布于北京
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[数项级数的基本概念及其性质.ppt

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[数项级数的基本概念及其性质

一、常数项级数的概念 1. 计算圆的面积正六边形的面积正十二边形的面积正形的面积数项级数的基本概念及其性质 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1. 级数的定义: (常数项)无穷级数一般项部分和数列级数的部分和 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2. 级数的收敛与发散: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 收敛发散发散发散综上 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解 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. 性质3 在一个级数中增加或删去有限个项不改变级数的敛散性，但会改变级数的和. 证明 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 注意收敛级数去括弧后所成的级数不一定收敛. 收敛发散 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 三、级数收敛的必要条件证明级数收敛的必要条件: 逆否命题： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 注意 1.如果级数的一般项不趋于零,则级数发散; 发散 2.必要条件不充分. 发散！ 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6 证明级数是发散的：证　级数的通项因为 ≠0，所以该级数发散 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例7 判别级数的敛散性：证　注意到通项 un= ，当n→∞时极限不存在，所以级数发散. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.