Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition
5th Edition
ISBN: 9780133311617
Author: Prentice Hall
Publisher: Prentice Hall
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Use the Limit Comparison Test to determine the convergence or divergence of the series.
n*(n* + 2)
4
n = 1
1
4
n*(n
4
+ 2)
= L > 0
lim
n → 00
converges
O diverges
8
determine whether the series converges or diverges using either the comparison test, ratio test, test for divergence, alternating series or the absolute convergence test For full credit, write your answer and clearly state your conclusion.
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- What is the use of conditional convergence and absolute convergence of an oscillating or alternating series? Explain this..arrow_forwardSuppose the series Ean converges and an> 0 for all n. (a) what can be said about the series Ea?? Give a reason for your answer. 1+an (b) what can be said about the series Σ? Give a reason for your answer. Hint: Note that we have limn→∞ an = 0. Comparison Theo- rem may be helpful.arrow_forwardConsider a sequence an such that the series an converges. n=0 (a) Explain, using words, why En=0 an+1000 Converges. (b) Assume that an is positive for all n. Explain, using words, whyEo an converges. (Hint: think about the comparison test.) (c) By providing an example show that, if an is allowed to be negative, n-0 an can diverge. (Hint: try an alternating series.)arrow_forward
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