Test the series for convergence or divergence using the Alternating Series Test.(-1)" -1Σ4 + 7nn = 1Identify b,Evaluate the following limit.lim b.'nSince lim b?O and b, +1?v b, for all n, ---Select--->

Questions from alternating series.

Answered: Test the series for convergence or…

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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00 (3n) 7nin Does the series (-1)- converge absolutely, converge conditionally, or diverge? n=1] Choose the correct answer below and, if necessary, fill in the answer box to complete your choice OA. The series converges absolutely because the corresponding series of absolute values is geometric with [r]= OB. The series converges conditionally per the Alternating Series Test and because the limit used in the Root Test is OC. The series converges conditionally per Alternating Series Test and because the limit used in the Ratio Test is D. The series diverges because the corresponding series of absolute values is a p-series with p= OE. The series converges absolutely because the limit used in the Ratio Test is OF. The series diverges because the limit used in the nth-Term Test is different from zero
x" Find the interval of convergence of the series п! n=0 O A. (-00, 0) Ов. (-1,1) Oc. [-1, 1] D. [-2, 2] Е. [-3, 3]
by simolofo alto adds grisos This question concerns the series 1 √n² +3 v by have to en hus 3 n=1 For each of the following tests, either use the test to show that the series is convergent or to show that it is divergent, or explain why the test cannot be used to do this, justifying your answer carefully. (a) The Non-null Test. (b) The Ratio Test. (c) The Limit Comparison Test. Xieng VAN IST 20 se
Σαπ M n=1 an = Σ n=1 3n+n 6"+In(n) We want to use the limit comparison test to determine whether this series converges or diverges. (a) The dominant term of the numerator is The dominant term of the denominator is We should therefore use b = We get an L= lim n+oo bn == (b) Which of the following statement is true for the series b₁₁? n=1 A. The series diverges by the nth term test for convergence. OB. The series converges by the geometric series test since -1 1. E. The series diverges by the geometric series test since r = F. none of the above >1 (c) What does the limit comparison test tell you about the series A. The test tells us no information OB. The series diverges C. The series converges D. none of the above +∞0 Σ 3" + n¹ 6n+ln(n) ? n=1
How do we get the limit 1 here.
00 8"+4 Consider the series >. an where an n=1 ng"-4 Compute the limit: an+1 lim (Enter "infinity" or "inf" if the limit is infinity; enter "DNE" if the limit does not exist for another reason.) an n→00 Given your answer above, what does the ratio test tell you about the series?
2n Зп - 1 Consider the series --Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE". 6n + 3 n=1 lim Vla, = L n00 Answer: L = What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: choose one Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent". Answer: choose one

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Test the series for convergence or divergence using the Alternating Series Test. (-1)" - 1 Σ 4 + 7n n = 1 Identify b, Evaluate the following limit. lim b. 'n Since lim b ? O and b, +1? v b, for all n, ---Select---