A6. Let 1 an be a series. (a) State precisely what is meant by the phrase "-1 an converges". (b) State precisely what is meant by the phrase "1 an converges absolutely". (c) Determine which of the following series converge absolutely. Briefly explain your answer. (i) Σ1(−1)"}. (ii) Σ1(−1)″ n²+1° (iii) Σ1(−1)n-1, -1 3n n!+1*

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A6. Let 1 an be a series.
n=1
(a) State precisely what is meant by the phrase "-1 an converges".
(b) State precisely what is meant by the phrase "1 an converges absolutely".
(c) Determine which of the following series converge absolutely. Briefly explain your
answer.
(i) Ex-₁(-1)" 1/1.
(ii) Σ1(−1)″ n²+1°
(iii) Σ1(−1)n-1,
-1 3n
n!+1'
Transcribed Image Text:A6. Let 1 an be a series. n=1 (a) State precisely what is meant by the phrase "-1 an converges". (b) State precisely what is meant by the phrase "1 an converges absolutely". (c) Determine which of the following series converge absolutely. Briefly explain your answer. (i) Ex-₁(-1)" 1/1. (ii) Σ1(−1)″ n²+1° (iii) Σ1(−1)n-1, -1 3n n!+1'
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