3. Consider the sequence {u}?, = {1,- - 1 1 - 1 2 '3' 4'5' 6 Select the true statement: A The sequence {ak} and the series as both diverge. B The sequence {ak} converges, but the series as diverges. c The sequence {ax} diverges, but the series ak converges. D The sequence {ak} and the series ak both converge. E None of the above.
Determine whether the following series converges absolutely, converges conditionally, or diverges. 00 (-1)+1e 3k Σ-11: -Σ ak (k 17 k 1 k 1 Find lim a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. koo O A. lim ak koo O B. The Ilimit does not exist. (1)* 1 (k 17) 3k e Σ. Now, let denote What can be concluded from this result using the Divergence Test? k 1 O...
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))
(4) Let Σ ak and Σ bk be series with positive terms. The limit comparison test applies when a/bk L0; suppose for this problem that ak/bk0. (a) Show that if Σ bk converges, then Σ ak converges. Hint: remember we can delete finitely many terms from the series and not affect convergence. Use the fact a/bk0 to truncate the series at a convenient point. (b) Show that if ak diverges, then bk diverges. (c) Show by example that if Σ...
show all work | 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
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...
2. Consider the sequence {2(-1)"}=1 (a) List the first 4 terms. (b) Compute for the partial sum of SA (e) Determine if the series converge or diverge. If it does converge what value it converges to. 00 2-3) nal
2 2) Suppose Ekoax(x - 1)* diverges when x = -2. Then a) Ekro ak must converge b) EX=0 Qr must diverge c) ak could converge or diverge Select the best choice and explain your reasoning.
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...
QUESTION 17 Which statement is true, concerning the series 7 + 1 3n2 - 1 and (2) 2n +1 3.22n-1 ? ОА (1) diverges, (2) converges. ОВ. (1) converges conditionally, (2) diverges. ос. Both diverge. OD (1) converges, (2) diverges. OE Botlı converge