Test the series for convergence or divergence using the Alternating Series Test.VnE(-1)"_3n + 5n = 1Identify bn:Evaluate the following limit.lim bnn→ 00Since lim b, ? v0 and bn + 1b, for all n > 2, ---Select---nn- 00

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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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1 Expand the function 4+5x in a power series E anx" with center c = 0. Find a,x". n=0 (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anx" DNE Incorrect Determine the interval of convergence. (Give your answers as intervals in the form (*, *). Use symbol ∞ for infinity, u for combining intervals, and appropriate type of parenthesis " (", ") " [" or "] " depending on whether the interval is open or closed. Enter DNE if interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E DNE Incorrect
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.
6
Suppose the series Zbx" converges for |x|9 n=1 4
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
Test the series for convergence or divergence using the Alternating Series Test. 9n - 5 E(-1)" 2n + 5 n = 1 Identify bn. Evaluate the following limit. lim bn n→∞ Since lim b, a o and bn + 1 O b, for all n, ? ? ---Select--- in

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Test the series for convergence or divergence using the Alternating Series Test. Vn E(-1)". 3n + 5 n = 1 Identify bn: Evaluate the following limit. lim b n n→ 00 Since lim b, ? v0 and bn + 1 b, for all n > 2, ---Select--- n n- 00