sec11_2

sec11_2 - 11.2 Series 1. Series Definitions 1.1. (1) If { a...

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Unformatted text preview: 11.2 Series 1. Series Definitions 1.1. (1) If { a n } n =1 is a sequence, then a 1 + a 2 + a 3 + = n =1 a n = a n is an (infinite) series . (2) The k-th partial sum is s k = a 1 + a 2 + a 3 + + a k = k n =1 a n (3) The sum of the series n =1 a n is determined by (4) The series is called convergent if the limit in 3 is a real number and this real number is the sum of the series . If the limit is not a real number the series is called divergent . (5) The k-th remainder term of the series n =1 a n is R k = a k +1 + a k +2 + a k +3 + = n = k +1 a n Remark 1.1. n =1 a n = s k + R k Example 1.1. Determine whether the series is convergent or divergent and if con- vergent determine the sum. n =1 1 2 n 1 Section 11.2 Series 2 2. Geometric Series Definition 2.1. A series of the form n =1 ar n- 1 is called a geometric series . r is called the common ratio ....
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This note was uploaded on 03/14/2011 for the course MAC 2312 taught by Professor Zhang during the Fall '07 term at FSU.

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sec11_2 - 11.2 Series 1. Series Definitions 1.1. (1) If { a...

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