Homework Answers
The given series satisfies all the conditions of alternating series test hence, the series is convergent.
and The series is Absolutely convergent.
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a,b,c and d
(-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove...
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- s...
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- solutely; (i) Show that the series satisfies all conditions of the Alternating Series Test; (ii) Find the partial sum sy of the series, and then estimate its remainder Ra: (iv) Determine how many terms are needed to approximate the sum of the series accurate to within 0.001, and then find this approximation. (a) L (b) Σ 27! 6. For each given series, complete the...
1. (Alternating Series Test.) This shows that for this particular sort of alternating series, the error...
1. (Alternating Series Test.) This shows that for this particular sort of alternating series, the error in approximating the infinite sum by a partial sum is at most the first omitted term. Suppose that aj > a2 > a3 > ... > 0 and that limnyoo An = 0. Let sn = {k=1(-1)kak. (a) Prove that if n > m > 0 then |sn – Sm! < am+1. (b) Prove that 2-1(-1)kak converges and that, for all n > 0,...
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equa...
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22...
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
(1 pt) Test each of the following series for convergence by either the Comparison Test or...
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV If it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does...
1 2 3
n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
(1 point) For each of the series below select the letter from a to c that best applies and the le...
(1 point) For each of the series below select the letter from a to c that best applies and the letter from d to j that best applies. A possible correct answer is af, for example. A. The series is absolutely convergent. B. The series converges, but not absolutely C. The series diverges D. The alternating series test shows the series converges. E. The series is a p-series F. The series is a geometric series. G. We can decide whether...
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It...
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It 2n=1 have to check that - trust me on this one.) (2n+1) (a) Use a calculator to evaluate the partial sum S3 of this series. Give the answer rounded to four decimal places. (b) Estimate the error of using S3 as an approximation to the sum of the series, i.e. estimate the remainder R3. Recall that the remainder estimate of the Alternating Series Test...
Test the series for convergence or divergence. 00 (-1)" +1 2n? n = 1 converges diverges...
Test the series for convergence or divergence. 00 (-1)" +1 2n? n = 1 converges diverges If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.00005. (If the quantity diverges, enter DIVERGES.) terms Need Help? Read It Watch It Talk to a Tutor Submit Answer Viewing Saved Work Revert to Last Response
Determine if the series 2n=1(-1)"(1 – 2n)" converges (C) or diverges (D). Justify your conclusion for...
Determine if the series 2n=1(-1)"(1 – 2n)" converges (C) or diverges (D). Justify your conclusion for C or D by showing all your work and indicating all test names that you used and conditions for conclusions. NO justification, NO credit! (Test names : Geo, NT, IT(P — series test), DCT, LCT, ACT, AST, RT, NRT)
6. For each given series, complete the following tasks: (i) Prove that the series converges ab- solutely; (i) Show that the series satisfies all conditions of the Alternating Series Test; (ii) Find the partial sum sy of the series, and then estimate its remainder Ra: (iv) Determine how many terms are needed to approximate the sum of the series accurate to within 0.001, and then find this approximation. (a) L (b) Σ 27! 6. For each given series, complete the...
1. (Alternating Series Test.) This shows that for this particular sort of alternating series, the error in approximating the infinite sum by a partial sum is at most the first omitted term. Suppose that aj > a2 > a3 > ... > 0 and that limnyoo An = 0. Let sn = {k=1(-1)kak. (a) Prove that if n > m > 0 then |sn – Sm! < am+1. (b) Prove that 2-1(-1)kak converges and that, for all n > 0,...
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
E) The series Σ-(-1)" 2- n a. converges conditionally. b. diverges by the nth term test. c. converges absolutely, d. converges by limit comparison test. F) The sum of the series 2-3)" is equal to e. None of the above
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV If it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
1 2 3
n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
(1 point) For each of the series below select the letter from a to c that best applies and the letter from d to j that best applies. A possible correct answer is af, for example. A. The series is absolutely convergent. B. The series converges, but not absolutely C. The series diverges D. The alternating series test shows the series converges. E. The series is a p-series F. The series is a geometric series. G. We can decide whether...
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It 2n=1 have to check that - trust me on this one.) (2n+1) (a) Use a calculator to evaluate the partial sum S3 of this series. Give the answer rounded to four decimal places. (b) Estimate the error of using S3 as an approximation to the sum of the series, i.e. estimate the remainder R3. Recall that the remainder estimate of the Alternating Series Test...
Test the series for convergence or divergence. 00 (-1)" +1 2n? n = 1 converges diverges If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.00005. (If the quantity diverges, enter DIVERGES.) terms Need Help? Read It Watch It Talk to a Tutor Submit Answer Viewing Saved Work Revert to Last Response
Determine if the series 2n=1(-1)"(1 – 2n)" converges (C) or diverges (D). Justify your conclusion for C or D by showing all your work and indicating all test names that you used and conditions for conclusions. NO justification, NO credit! (Test names : Geo, NT, IT(P — series test), DCT, LCT, ACT, AST, RT, NRT)
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