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Ratio Test Zn+1 If a series z1 + z2 + •… with zn + 0 (n = 1, 2, .) is such that lim then: = L. Zn (a) If L< 1, the series converges absolutely. (b) If L> 1, the series diverges. (c) If L = 1, the series may converge or diverge, so that the test fails and permits no conclusion.

Ratio Test Zn+1 If a series z1 + z2 + •… with zn + 0 (n = 1, 2, .) is such that lim then: = L. Zn (a) If L< 1, the series converges absolutely. (b) If L> 1, the series diverges. (c) If L = 1, the series may converge or diverge, so that the test fails and permits no conclusion.

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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Ratio Test Zn+1 = L, If a series z1 + z2 + • ·· with zn # 0 (n = 1, 2, ·.) is such that lim then: %D Zn (a) If L< 1, the series converges absolutely. (b) If L > 1, the series diverges. (c) If L = 1, the series may converge or diverge, so that the test fails and permits no conclusion.
Transcribed Image Text:Ratio Test Zn+1 = L, If a series z1 + z2 + • ·· with zn # 0 (n = 1, 2, ·.) is such that lim then: %D Zn (a) If L< 1, the series converges absolutely. (b) If L > 1, the series diverges. (c) If L = 1, the series may converge or diverge, so that the test fails and permits no conclusion.
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