# Calc09_5 - 9.5 Testing Convergence at Endpoints Petrified...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ?...
View Full Document

## This note was uploaded on 02/12/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

### Page1 / 21

Calc09_5 - 9.5 Testing Convergence at Endpoints Petrified...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online