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Unformatted text preview: 9.5 Testing Convergence at Endpoints Petrified Forest National Park, Arizona Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 Remember: The series converges if . 1 L < The series diverges if . 1 L The test is inconclusive if . 1 L = The Ratio Test : If is a series with positive terms and n a ∑ 1 lim n n n a L a + →∞ = then: → This section in the book presents several other tests or techniques to test for convergence, and discusses some specific convergent and divergent series. → The series converges if . 1 L < The series diverges if . 1 L The test is inconclusive if . 1 L = Nth Root Test : If is a series with positive terms and n a ∑ lim n n n a L →∞ = then: Note that the rules are the same as for the Ratio Test. → example: 2 1 2 n n n ∞ = ∑ 2 2 n n n 2 2 n n = 2 lim n n n →∞ ( 29 2 lim n n n →∞ = ? → lim n n n →∞ 1 lim n n n →∞ ( 29 1 lim ln n n n e →∞ 1 lim ln n n n e →∞ ln lim n n n e →∞ 1 lim 1 n n e →∞ e 1 Indeterminate, so we use L’Hôpital’s Rule formula #104 formula #103 → example: 2 1 2 n n n ∞ = ∑ 2 2 n n n 2 2 n n = 2 lim 2 n n n →∞ 2 lim n n n →∞ ( 29 2 lim n n n →∞ = 2 1 = 1 = 1 2 = ∴ it converges ?...
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 Spring '08
 Smith
 Mathematical Series, lim

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