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To test for convergence or divergence of the series an, the ratio test computes the limit an+1 R= lim an (*) If 0 < R < 1, then the series converges absolutely. If R > 1, the series diverges. If R = 1, then the limit comparison test is inconclusive, meaning that Ean may (1) absolutely converge; (2) conditionally converge; or (3) diverge. For each possibility, give an example of a series such that the calculated limit by (*) evaluates to one, so that the ratio test is inconclusive.

To test for convergence or divergence of the series an, the ratio test computes the limit an+1 R= lim an (*) If 0 < R < 1, then the series converges absolutely. If R > 1, the series diverges. If R = 1, then the limit comparison test is inconclusive, meaning that Ean may (1) absolutely converge; (2) conditionally converge; or (3) diverge. For each possibility, give an example of a series such that the calculated limit by (*) evaluates to one, so that the ratio test is inconclusive.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) absolutely convergent series

b) conditionally convergent series

c) divergent series

7. To test for convergence or divergence of the series E an, the ratio test computes the limit an+1 R= lim (*) an If 0 < R < 1, then the series converges absolutely. If R > 1, the series diverges. If R = 1, then the limit comparison test is inconclusive, meaning that Can may (1) absolutely converge; (2) conditionally converge; or (3) diverge. For each possibility, give an example of a series such that the calculated limit by (*) evaluates to one, so that the ratio test is inconclusive.
Transcribed Image Text:7. To test for convergence or divergence of the series E an, the ratio test computes the limit an+1 R= lim (*) an If 0 < R < 1, then the series converges absolutely. If R > 1, the series diverges. If R = 1, then the limit comparison test is inconclusive, meaning that Can may (1) absolutely converge; (2) conditionally converge; or (3) diverge. For each possibility, give an example of a series such that the calculated limit by (*) evaluates to one, so that the ratio test is inconclusive.
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