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2 ,-n² and convergence of an where an what do you conclude about the series? ne

2 ,-n² and convergence of an where an what do you conclude about the series? ne

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Which test do you use to decide the -n² convergence of an where an what do you conclude about the series? = ne and Use the limit comparison test with b, An n²e-n°.Then lim = ∞, and since n→∞ b, Σb, is (D), Σ α, is (D). Use the limit comparison test with bn An e-n. Then lim n→∞ bn 0, and since Σ, is (D) Σ α, is (D). None of the given options is correct. -n² Write e as cos n2 + i sin n² and apply the alternating series test to the real and imaginary parts separately. Since each term is decreasing in magnitude and tending to zero, the series is (C) by the AST.
Transcribed Image Text:Which test do you use to decide the -n² convergence of an where an what do you conclude about the series? = ne and Use the limit comparison test with b, An n²e-n°.Then lim = ∞, and since n→∞ b, Σb, is (D), Σ α, is (D). Use the limit comparison test with bn An e-n. Then lim n→∞ bn 0, and since Σ, is (D) Σ α, is (D). None of the given options is correct. -n² Write e as cos n2 + i sin n² and apply the alternating series test to the real and imaginary parts separately. Since each term is decreasing in magnitude and tending to zero, the series is (C) by the AST.
O Use the integral test with f (x) = xe' N f(x) dx → 1 -1 e as N → .Then 2 1 0. Further, f(x) is positive and decreasing for x > 1, so the series is (C) by the integral test. ,2 „x- Use the integral test with f(x) = xe ¢N . Then 1/ → ∞ as. f (x) dx o as N → o. Therefore the series is (D) by the integral test.
Transcribed Image Text:O Use the integral test with f (x) = xe' N f(x) dx → 1 -1 e as N → .Then 2 1 0. Further, f(x) is positive and decreasing for x > 1, so the series is (C) by the integral test. ,2 „x- Use the integral test with f(x) = xe ¢N . Then 1/ → ∞ as. f (x) dx o as N → o. Therefore the series is (D) by the integral test.
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