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Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine w...
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13 n8n (i) Determine whether ah...
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13 n8n (i) Determine whether ah diverges. If the sequence converges, find its converges or limit. o0 (ii) Determine whether r diverges. Justify your ansv swer an Converges o n-1 (b) Consider the series (2n)! 2 (n!) and determine whether it converges or diverges. Justify your answer IM8 8
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13...
What is the limit of the sequence -1 sin 1 Does not converge 21 12 1 What is the sum of 13 13 12 1 13 None of the above...
What is the limit of the sequence -1 sin 1 Does not converge 21 12 1 What is the sum of 13 13 12 1 13 None of the above 3) 2 5/2 Evaluate 0 7n 125/2 4) 2 (ln n true false The series converges 5) 2n2 1 The series converges The series diverges. 3n36 Using the limit comparison test The test is inconclusive determine whether the series converges or diverges.
What is the limit of the sequence -1...
(a) (6 marks) Does the series (–19* sin( , ) converge or divergor Justi (a) (6...
(a) (6 marks) Does the series (–19* sin( , ) converge or divergor Justi (a) (6 marks) Does the series converge or diverge? Justify your answer and state any test(s) you used. (-1)" cos(4n) (b) (2 marks) Consider the series . Explain why the Alternating Series Test can NOT be consider the senes 2 2n3 . used to determine whether the series converges or diverges.
Question 1 3+cos(n) 2n X Which of the following properties hold for the sequence an for...
Question 1 3+cos(n) 2n X Which of the following properties hold for the sequence an for n 2 1? l. Bounded Il. Monotonic IIl. Convergent Selected Answer a. I only a. I only b. Il only c. I and Il only d. I and Ill only e. I, II, and III Remember what these conditions mean: Bounded means all terms of the sequence have to lie within a specific range of values. Monotonic means the sequence is ALWAYS increasing or...
show all work | 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing...
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| 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
QUESTION 1 n a) Determine whether the sequence converges or diverges. n1 (3 marks)
QUESTION 1 n a) Determine whether the sequence converges or diverges. n1 (3 marks)
(1 point) Determine whether the sequence a Converges (w/n Limit if it exists, blank otherwise): 17...
(1 point) Determine whether the sequence a Converges (w/n Limit if it exists, blank otherwise): 17 + 2 10n + 5 converges or diverges. If it converges, find the limit. (point) Find the first six terms of the recursively defined sequence 5.45-1 + 1 for n > 1. and = 1 first six terms (Enter your answer as a comma-separated list.)
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and...
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and if it converges, find the limit. Find the length of the curve defined by x = 2t3, y = 3t2, osts 1.
Page 13 of 15 Previous 13) 00 Determine whether the series m converges or diverges. n1...
Page 13 of 15 Previous 13) 00 Determine whether the series m converges or diverges. n1 a) Diverges b) converges Both converges and diverges d) No test is applicable 1) Determine whether the sequence converges or diverges. In case of convergence find its limit. n + 2 Converges, lim = 8 b) Converges, lim = 7 Converges, lim - 4 d) Diverges
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly...
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly increasing and converges to zero; ii. a sequence of real numbers that is not monotonic and converges to 2 iii. a sequence of real numbers that is bounded and divergent. (d) (5 marks) Calculate the first four terms in the Laurent series representation of e*.
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13 n8n (i) Determine whether ah diverges. If the sequence converges, find its converges or limit. o0 (ii) Determine whether r diverges. Justify your ansv swer an Converges o n-1 (b) Consider the series (2n)! 2 (n!) and determine whether it converges or diverges. Justify your answer IM8 8
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13...
What is the limit of the sequence -1 sin 1 Does not converge 21 12 1 What is the sum of 13 13 12 1 13 None of the above 3) 2 5/2 Evaluate 0 7n 125/2 4) 2 (ln n true false The series converges 5) 2n2 1 The series converges The series diverges. 3n36 Using the limit comparison test The test is inconclusive determine whether the series converges or diverges.
What is the limit of the sequence -1...
(a) (6 marks) Does the series (–19* sin( , ) converge or divergor Justi (a) (6 marks) Does the series converge or diverge? Justify your answer and state any test(s) you used. (-1)" cos(4n) (b) (2 marks) Consider the series . Explain why the Alternating Series Test can NOT be consider the senes 2 2n3 . used to determine whether the series converges or diverges.
Question 1 3+cos(n) 2n X Which of the following properties hold for the sequence an for n 2 1? l. Bounded Il. Monotonic IIl. Convergent Selected Answer a. I only a. I only b. Il only c. I and Il only d. I and Ill only e. I, II, and III Remember what these conditions mean: Bounded means all terms of the sequence have to lie within a specific range of values. Monotonic means the sequence is ALWAYS increasing or...
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| 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
QUESTION 1 n a) Determine whether the sequence converges or diverges. n1 (3 marks)
(1 point) Determine whether the sequence a Converges (w/n Limit if it exists, blank otherwise): 17 + 2 10n + 5 converges or diverges. If it converges, find the limit. (point) Find the first six terms of the recursively defined sequence 5.45-1 + 1 for n > 1. and = 1 first six terms (Enter your answer as a comma-separated list.)
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and if it converges, find the limit. Find the length of the curve defined by x = 2t3, y = 3t2, osts 1.
Page 13 of 15 Previous 13) 00 Determine whether the series m converges or diverges. n1 a) Diverges b) converges Both converges and diverges d) No test is applicable 1) Determine whether the sequence converges or diverges. In case of convergence find its limit. n + 2 Converges, lim = 8 b) Converges, lim = 7 Converges, lim - 4 d) Diverges
(c) (5 marks) Give an example of i. a sequence of real numbers that is strictly increasing and converges to zero; ii. a sequence of real numbers that is not monotonic and converges to 2 iii. a sequence of real numbers that is bounded and divergent. (d) (5 marks) Calculate the first four terms in the Laurent series representation of e*.
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