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α (2) Σ n=1 (b) n=1 2n³ +5 2η3 4n³ - 1 n23n (n + 4)n!

α (2) Σ n=1 (b) n=1 2n³ +5 2η3 4n³ - 1 n23n (n + 4)n!

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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When studying sequences in Unit D2, we made great use of a library of basic sequences. You will now see that there is also a library of basic series whose convergence or divergence is known. We can determine the convergence or divergence of a large number of other series from these basic series by using our tests. Theorem D33 Basic series The following series are convergent: (a) for p > 2 n=1 (c) (b) Σc", for Osc<1 n=1 n=1 nP n=1 (d) n! The following series is divergent: (e) for 0 < p ≤ 1. n=1 nen, for p > 0, 0≤ c < 1 for c ≥ 0. nP
Transcribed Image Text:When studying sequences in Unit D2, we made great use of a library of basic sequences. You will now see that there is also a library of basic series whose convergence or divergence is known. We can determine the convergence or divergence of a large number of other series from these basic series by using our tests. Theorem D33 Basic series The following series are convergent: (a) for p > 2 n=1 (c) (b) Σc", for Osc<1 n=1 n=1 nP n=1 (d) n! The following series is divergent: (e) for 0 < p ≤ 1. n=1 nen, for p > 0, 0≤ c < 1 for c ≥ 0. nP
Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) (b) M8 M8 n=1 2n³ +5 4n³ - 1 n²3n (n + 4)n!
Transcribed Image Text:Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) (b) M8 M8 n=1 2n³ +5 4n³ - 1 n²3n (n + 4)n!
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