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Unformatted text preview: 9.5 Testing Convergence at Endpoints Greg Kelly, Hanford High School, Richland, Washington The original Hanford High School, Hanford, Washington 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 LHpitals 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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This note was uploaded on 03/10/2008 for the course MATH 214 taught by Professor Riggs during the Fall '05 term at Cal Poly Pomona.
 Fall '05
 Riggs
 Differential Calculus

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