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Ints) Find an alternating series which satisfies part 1 but not part 2 of the AST (5 po and diver...
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the...
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
(2+3+1+1+1=8 points) Roughly, the Limit Comparison Test allows one to determine whether a given DO series...
(2+3+1+1+1=8 points) Roughly, the Limit Comparison Test allows one to determine whether a given DO series an converges or diverges based on the computation of the limit an L = lim no ba 00 where on is another series. In this exercise, the Limit Comparison Test is used to determine whether the series shown below converges or diverges: yาง m4 +5n - 4 1. Write your choice of bn (Your answer should be in terms of n and simplified fully.)...
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diver...
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diverges and bn diverges, then (an + bn) diverges. (j) A power series always converges at at least one point. (l) The series from ∞ to n=1 2^ (−1)^n converges?
Consider the series 2 Which of the following statements are true? (Select all that apply). Yanitiniz:...
Consider the series 2 Which of the following statements are true? (Select all that apply). Yanitiniz: The series absolutely converges. (-1)" lim 8+ = 0 The series converges conditionally It is an alternating series. The series converges to some finite number The series conditionally and absolutely converges. tale) diverse diverges. It is not an alternating series. The ratio test is inconclusive.
00 Determine whether the series 2" +5" 6 converges or diverges. If it converges, find its...
00 Determine whether the series 2" +5" 6 converges or diverges. If it converges, find its sum. n=1 Select the correct answer below and, if necessary, fill in the answer box within your choice. O A. The series diverges because it is the sum of two geometric series, at least one with In 21. The series converges because it is the sum of two geometric series, each with (r< 1. The sum of the series is OB (Simplify your answer.)...
Problem 5. (1 point) Consider the series = 4+(-1)^n). 63 - 3n Which of the following...
Problem 5. (1 point) Consider the series = 4+(-1)^n). 63 - 3n Which of the following statements accurately describes the series? A. The series diverges by the Divergence Test. B. The series converges by the Limit Comparison Test with the series 613 C. The series converges by the Alternating Series Test. D. The series diverges by the Integral Test. E. The series converges by the Integral Test. Problem 6. (1 point) In order to determine the convergence or divergence of...
Study: Ch. 5 5.2 #93-96, 5.5 280-285 The given series converges by Alternating Series Test. Use...
Study: Ch. 5 5.2 #93-96, 5.5 280-285 The given series converges by Alternating Series Test. Use the estimate |RN| <bn+1 to find the least value of N that guarantees that the sum Sy differs from the infinite sum n n=1 by at most an error of 0.01. Answer (a) What is N? (b) What is Sy and what is the actual sum S of the series? (c) Is S - SN <0.01?
all part of one question Determine whether the following series converges absolutely, converges conditionally, or diverges....
all part of one question
Determine whether the following series converges absolutely, converges conditionally, or diverges. OD (-1)"ax= k1 k=1 Vk 14 +9 Find lim ak. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. k-20 OA. lim ax - OB. The limit does not exist. (-1*45 Now, let a denote E What can be concluded from this result using the Divergence Test? 14 k=1 Vk +9 O A. The series Elak...
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately...
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately describes the series? A. The series converges by the Integral Test. B. The series diverges by the Divergence Test. C. The series converges by the Alternating Series Test. 8W 5 D. The series converges by the Limit Comparison Test with the series 6 6n3 n=1 O E. The series diverges by the Integral Test.
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately...
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately describes the series? A. The series converges by the Integral Test. B. The series diverges by the Divergence Test. C. The series converges by the Alternating Series Test. 8W 5 D. The series converges by the Limit Comparison Test with the series 6 6n3 n=1 O E. The series diverges by the Integral Test.
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
(2+3+1+1+1=8 points) Roughly, the Limit Comparison Test allows one to determine whether a given DO series an converges or diverges based on the computation of the limit an L = lim no ba 00 where on is another series. In this exercise, the Limit Comparison Test is used to determine whether the series shown below converges or diverges: yาง m4 +5n - 4 1. Write your choice of bn (Your answer should be in terms of n and simplified fully.)...
Consider the series 2 Which of the following statements are true? (Select all that apply). Yanitiniz: The series absolutely converges. (-1)" lim 8+ = 0 The series converges conditionally It is an alternating series. The series converges to some finite number The series conditionally and absolutely converges. tale) diverse diverges. It is not an alternating series. The ratio test is inconclusive.
00 Determine whether the series 2" +5" 6 converges or diverges. If it converges, find its sum. n=1 Select the correct answer below and, if necessary, fill in the answer box within your choice. O A. The series diverges because it is the sum of two geometric series, at least one with In 21. The series converges because it is the sum of two geometric series, each with (r< 1. The sum of the series is OB (Simplify your answer.)...
Problem 5. (1 point) Consider the series = 4+(-1)^n). 63 - 3n Which of the following statements accurately describes the series? A. The series diverges by the Divergence Test. B. The series converges by the Limit Comparison Test with the series 613 C. The series converges by the Alternating Series Test. D. The series diverges by the Integral Test. E. The series converges by the Integral Test. Problem 6. (1 point) In order to determine the convergence or divergence of...
Study: Ch. 5 5.2 #93-96, 5.5 280-285 The given series converges by Alternating Series Test. Use the estimate |RN| <bn+1 to find the least value of N that guarantees that the sum Sy differs from the infinite sum n n=1 by at most an error of 0.01. Answer (a) What is N? (b) What is Sy and what is the actual sum S of the series? (c) Is S - SN <0.01?
all part of one question
Determine whether the following series converges absolutely, converges conditionally, or diverges. OD (-1)"ax= k1 k=1 Vk 14 +9 Find lim ak. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. k-20 OA. lim ax - OB. The limit does not exist. (-1*45 Now, let a denote E What can be concluded from this result using the Divergence Test? 14 k=1 Vk +9 O A. The series Elak...
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately describes the series? A. The series converges by the Integral Test. B. The series diverges by the Divergence Test. C. The series converges by the Alternating Series Test. 8W 5 D. The series converges by the Limit Comparison Test with the series 6 6n3 n=1 O E. The series diverges by the Integral Test.
(1 point) Consider the series 5+(-1)"n3 6n3 – In n=1 Which of the following statements accurately describes the series? A. The series converges by the Integral Test. B. The series diverges by the Divergence Test. C. The series converges by the Alternating Series Test. 8W 5 D. The series converges by the Limit Comparison Test with the series 6 6n3 n=1 O E. The series diverges by the Integral Test.
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