Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive.856kΣ k!k=1Choose the correct answer below.O A. The series diverges because lim00+X6kkl5O C. The series converges because lim00+x= 0.B. The series converges because lim = 0.k!k→∞o56k6k5k!56kk!#0.O D. The series diverges because lim #0.k→∞oE. The Divergence Test is inconclusive.

Given series is ∑k=1∞6k5k! Let Uk=6k5k!.

Answered: Use the Divergence Test to determine…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. ∞ 1 Σ n+11 n=0 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The series diverges because lim n→∞ B. The test is inconclusive because lim n→∞ C. The series diverges because lim n→∞ 1 n+11 D. The series diverges because lim n→∞ 1 n+11 1 n+11 exists and is equal to 1 n+11 = = ∞ and fails to exist. = ∞ and fails to exist.
Which of the following statement is true for the alternating series below? n=0 n3 +1 O The series diverges by Alternating Series test. O Alternating Series test cannot be used, because b,= 1 is not decreasing. n³ +1 none of the others. O Alternating Series test cannot be used, 1 #0. n+0o n°+1 because lim The series converges by Alternating Series test.
Consider the series an where n=1 (-5n - 3)" (-3n-5)" In this problem you must attempt to use the Root Test to decide whether the series converges. Compute an = Which of the following statements is true? A. The Root Test says that the series converges absolutely. B. The Root Test says that the series diverges. L = lim √√|an| 11-00 Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L= ✓ C. The Root Test says that the series converges conditionally. D. The Root Test is inconclusive, but the series converges absolutely by another test or tests. E. The Root Test is inconclusive, but the series diverges by another test or tests. F. The Root Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
Determine whether the series Σ e5n n=0 converges or diverges. If it converges, find its sum. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The series diverges because it is a geometric series with |r| 21. The series diverges because OB. lim e5n #0 or fails to exist. - n→∞ The series converges because k OC. lime5n fails to exist. k→∞ n=0 The series converges because lim e5n = 0. The sum of the OD. n→∞o series is (Type an exact answer.) The series converges because it is a geometric series with |r| < 1. O E. The sum of the series is (Type an exact answer.)
Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. ∞ 1 Σ n+19 n=0 Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The series diverges because lim n→∞ B. D. 1 non+19 The series diverges because lim 1 n+19 O c. The test is inconclusive because lim n→∞ The series diverges because lim n→∞ = ∞ and fails to exist. 1 n+19 exists and is equal to 1 n+19 = - ∞ and fails to exist.
a. Find the first four nonzero terms of the Maclaurin series for the given function. b. Write the power series using summation notation. c. Determine the interval of convergence of the series. f(x) = ( – 1 + x2) -1 a. The first nonzero term of the Maclaurin series is The second nonzero term of the Maclaurin series is The third nonzero term of the Maclaurin series is The fourth nonzero term of the Maclaurin series is b. Write the power series using summation notation. Choose the correct answer below. 00 OA. E(-1)5,2* k=0 O B. 2x* k=0

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Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. Σ k=1 5 6k k! Choose the correct answer below. O A. The series diverges because lim 00+X 5 6k kl = 0. 5 6k B. The series converges because lim = 0. k! k→∞o