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Question 1: (1 point) True or False? Choose true only if both the argument and answer...
Please show all steps. Question 2: (1 point) True or False? Choose true only if both the argument and answer is correct. The series 1 n=1 4n4 + 2n +1 is convergent because 0 VI 4n4 + 2n +1 4n4 for all n >1 and 00 jo 1 00 4 4n4 n=1 74 (series with general term 1 / TP with p=4>1). (a) True (b) False
Part A [15 Points]: Choose TRUE or FALSE for each of the following items. 1. If the series anx" converges, then anx" → as n 700. TRUE FALSE 2. The series & {-1}" is absolutely convergent. TRUE FALSE 3. The series 2 is convergent using the Ratio Test. TRUE FALSE 00 4. The series An- n n2+1 is convergent using the Geometric Series Test. TRUE FALSE 5. The series 2n=1 42+2n+3 (-1)" is conditionally convergent. TRUE FALSE
At least one of the answers above is NOT correct. (1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you...
Please only answer questions a, d, and f. Thank you. 1. True/False Explain. If true, provide a brief explanation and if false, provide a counterexample. Choose 3 to answer, if more than 3 are completed I will pick the most convenient 3. Given a sequence {an} with linn→alanF1, it follows that linnn→aA,-1. b. A series whose terms converge to 0 always converges. c. A sequence an converges if for some M< oo, an 2 M and an+1 >an for all...
6. True or False. If the statement is true, explain why using theorems/tests from class, and if the statement is false provide a counter example. (a) If an and are series with positive terms such that is divergent and an <by for all r, then an is divergent. I (b) If a, and be are series with positive terms such that is convergent and an <br for all 17, then an is convergent. (e) If lim 0+1 = 1 then...
(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent by using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed (Note: if the conclusion is true but the argument that led to it was wrong, you must enter l.) In(n) > 1, , and the...
Instructions: This assignment has three parts. Part A: True/False questions, Part B: Multiple choice questions, and Part C: Workout Problems. Part A (15 Points : Choose TRUE or FALSE for each of the following items. 1. If the series (-1)"an converges, then Ela, also converges. TRUE FALSE 2. The series is convergent by the Ratio Test. TRUE D FALSE 3. The series 2-1 n'e -- is convergent. TRUE FALSE 4. The series 1(-7)-" is absolutely convergent. TRUE FALSE 5. The...
1. State whether the following statements are true or false. Give reasons for your answer (a) If limko WR=0 then our converges (b) = 5 means that the partial sums converge to 5 (c) E U is called conditionally convergent if it satisfies the conditions of the alternating series test (d) The limit comparison test applies only to series which are positive from some point on (e) (-2)* = 5 (f) If uk = (2k + 1)! then uk+1 =...
An argument is valid ONLY when both its premises and conclusion are true. True or false?
(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (or "correct") if the argument is valid, or enterI (for "incorrect") if any part of the argument is flawed (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) 1. For all n^ 1 arctan(n 2....