lec 15 - Tuesday, January 31 Lecture 15 : Infinite series...

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Unformatted text preview: Tuesday, January 31 Lecture 15 : Infinite series (Refers to Section 8.2 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : Define an infinite series, define a partial sum of a series, define the limit of a series, define the geometric series and determine when it converges and when it diverges. 15.1 Definition An infinite series is an expression which takes the sum of all the terms in an infinite sequence while respecting the order. If { c i : i = 1 to } is an infinite sequence then we denote its associated infinite series by For now this expression has no meaning. In what follows we will define it and discuss methods for determining its value when it has one. The c i s are sometimes referred to as the summands . If n is any natural number, we define the n th partial sum , S n , of the series as the sum of the first n terms of the series, i.e., S n = i = 1 to n c i ....
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lec 15 - Tuesday, January 31 Lecture 15 : Infinite series...

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