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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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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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