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Unformatted text preview: A geometric series with ratio r diverges if 1 r . If 0< 1 < r , then the series converges to the sum r a S = 1 . Keep in mind that a is simply the first term of the series and r is the ratio. Examples: Nth Term Test for Divergence 8.2.2 If { does not converge to 0, then the series diverges. } n a n a Note that this is a test for divergence only. You can never say that a series converges by the nth term test. Furthermore, it is NOT an if and only if statement. Just because { does converge to 0 does not mean that the corresponding series converges. You would need to do more investigation. } n a Examples: Properties of Infinite Series If and and c is a real number, then the following series converge to the indicated sums. A a n = B b n = 1. cA ca n = 2. B A b a n n + = + ) ( 3. B A b a n n = ) ( Examples:...
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This note was uploaded on 01/13/2012 for the course MATH 2564 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.
 Spring '12
 PamelaSatterfield
 Infinite Series

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