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(1 point) The series is an alternating series but we can apply the ratio test to...
Homework 7: Problem 5 Previous Problem Problem List Next Problem (1 point) Applying the ratio test to the series = (x + 1)2.44 you would compute ak+1 lim "4+1 = lim 5/(k^2(1+(2/k)^2(16)) = 5/16 k->00 akk >00 Hence the series converges . Note that you will have to simplify your answer for the limit or you will get an error message.
Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. 00 П Σ no +1 Select the correct answer below and fill in the answer box to complete your choice. k-00 O A. According to the Divergence Test, the series converges because lim ak (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim ax = (Simplify your answer.) O c. The Divergence Test is inconclusive because limax...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
Test the series below for convergence using the Ratio Test. 10" 2n! The limit of the ratio test simplifies to lim f(n) where f(n) = Preview Preview The limit is: (enter oo for infinity if needed) Based on this, the series Converges Message instructor about this question
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. (Exercise 4.10, modified) Given a series Σ 1 ak with ak 0 for all k and lim Qk+1 k0oak we will prove that the series converges absolutely. (This is part of the ratio test sce the handout.) (a) Fix a valuc q with r <<1. Use the definition of r to prove that there exists a valuc N such that for any k 2 N. (b) Prove that Σο, laNIqk-1 converges, where N is the value from part (a)....
Problem 5. (1 point) Consider the series = 4+(-1)^n). 63 - 3n Which of the following statements accurately describes the series? A. The series diverges by the Divergence Test. B. The series converges by the Limit Comparison Test with the series 613 C. The series converges by the Alternating Series Test. D. The series diverges by the Integral Test. E. The series converges by the Integral Test. Problem 6. (1 point) In order to determine the convergence or divergence of...
- (-12 Points] DETAILS ROGACALCET4 10.5.012. MY NOTES ASK YOUR TEACHER PRACTIC Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive. 30 n n! nul p=lim n- an According to the Ratio Test, the series converges. According to the Ratio Test, the series diverges. O The test is inconclusive. 4. (-12 points) DETAILS ROGACALCET4 10.5.030 MY NOTES ASK YOUR TEACHER PRACTICE ANG Assume that oft converges to p = 1 and bn...
Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series. 00 (-1)"n Σ n²-8 n=3 Identify an Evaluate the following limit. lima n- Since lim 0 and an - 12va, for all n. ---Select- Submit Answer
Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. 00 n no 2n + 1 Select the correct answer below and fill in the answer box to complete your choice. k-00 k-00 O A. According to the Divergence Test, the series diverges because lim ax = (Simplify your answer.) OB. According to the Divergence Test, the series converges because lim ax = 1 (Simplify your answer.) OC. The Divergence Test is...