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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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 Spring '12
 PamelaSatterfield
 Calculus, Infinite Series, nth partial sum

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