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Series6

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الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 2
أستاذ المادة هدى عامر هادي       21/03/2021 21:24:54
In the previous lesson we studied the last two tests of convergence and divergence for Infinite Series. Now we are going to take a look at some specific kinds of series. In this lesson we are going to start talking about power series. We are going to use the infinite series to define a function and the most common series is the power series.
Def. A power series, is any series that can be written in the form,


where c and a_n are numbers. The? a?_n’s (a_1,a_2,a_3,…) are called the coefficients of the series.
The first thing to notice about a power series is that it is a function of x. That is different from any other kind of series that we’ve looked at to this point. In all the prior lessons we’ve only allowed numbers in the series and now we are allowing variables to be in the series as well. This will not change how things work. However, everything that we know about series still holds.


The Interval and Radius of Convergence
Consider the function f(x)=?_(n=0)^??a_n ?(x-c)?^n ? . The domain of this function is the set of those values of x for which the series is convergent. The domain of such function is called the interval of convergence.


If the interval is (c-R,c+R) for some R>0, (together with one or both of the endpoints), the R is called the radius of convergence. Convergence of the series at the endpoints is determined separately


المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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