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2 2) Suppose Ekoax(x - 1)* diverges when x = -2. Then a) Ekro ak must...
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...
(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...
3. Consider the sequence {ak} = 1 = 1. -1 1 -1 1 -1 2 5 6 Select co ܠܛ the true statement: A The sequence {ak} and the series Ļak both diverge. B. The sequence {ak} converges, but the series [ak diverges. c| The sequence {ak} diverges, but the series [ak converges. D| The sequence {ak} and the series ak both converge. E None of the above.
6. Suppose Σχο akrk converges when x-3 Give 2 other values of x for which Σ , akrk uppose Ž 0 aka.. converges when x = must converge. 8 7. Indicate if the following are always true or may be false (a) If lim a 0, then Cay converges. (b) If ak > bk 2 0 and Σ bk diverges, then Σ ak converges. (c) If ak > 0 and 'lim k-0, then Σ ak converges (d) If ak >...
1 point) Suppose that onE" converges whenz-4 and diverges when - 8. Determine whether the following series converge or diverge. Answer "Converges"or "Diverges. Note: You only have two attempts at this problem. converges ' 1, Cn Diverges 2 9 Converges 3. c(-10)" I-0 n-0 Diverges 3. (-1)"с, 12"
1 point) Suppose that onE" converges whenz-4 and diverges when - 8. Determine whether the following series converge or diverge. Answer "Converges"or "Diverges. Note: You only have two attempts at this problem....
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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...
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.
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0. a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. c) When x=−2, for what values of p does the series converge? Explain your reasoning. (d) When p=1 and x=3.1, the series converges to a value SS....
1 sin )-sin Determine whether the following series converge or diverge. +1 Select one a. Diverges b. Converges, and the partial sum is 1 C. Converges, and the partial sum is sin 1 2 d. Converges, and the partial sum is 0
Does the following series converge absolutely, converge conditionally or diverge? jo (-1)4+1 27k diverges converges absolutely converges conditionally Box 1: Select the best answer For the series below calculate find the number of terms n that must be added in order to find the sum to the indicated accuracy. 2 (-1)"+1) 2n3 +4 error] < 0.01 n= Preview Find the sum of the series correct to 2 decimal places. Sum = Preview Box 1: Enter your answer as a number...