Use Strategy D13 from Unit D3 to determine whether each of the followingseries converges. Name any results or rules that you use. You may use thebasic series listed in Theorem D33 from Unit D3.∞ 3n²-4 cos n4n4+1(c) Σn=1(d)∞n=1(-1)+1n²3n³ - 2 When studying sequences in Unit D2, we made great use of a library ofbasic sequences. You will now see that there is also a library of basic serieswhose convergence or divergence is known. We can determine theconvergence or divergence of a large number of other series from thesebasic series by using our tests.Theorem D33 Basic seriesThe following series are convergent:(a)for p > 2n=1(c)(b) Σc", for Osc<1n=1n=1nPn=1(d)n!The following series is divergent:(e)for 0 < p ≤ 1.n=1nen, for p > 0, 0≤ c < 1for c ≥ 0.nP

(b) Series is ∑n=1∞3n2-4cosn4n4+1≡∑an. By limit comparision test if ∑an and ∑bn are series of…

Answered: 8 (0) Σ n=1 (d) 8 Σ 3η2 – 4 cos 4n4 + 1…

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8 (0) Σ n=1 (d) 8 Σ 3η2 – 4 cos 4n4 + 1 2 (-1)^+1n² 3η3 – 2

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.2: Sequences, Series And Summation Notation

Problem 51E

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Question

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.
∞ 3n²-4 cos n
4n4+1
(c) Σ
n=1
(d)
∞
n=1
(-1)+1n²
3n³ - 2

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

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