Determine whether the following series converges or diverges (show your answer in detail). 00 k Σ...
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...
Determine whether the following series converges. Justify your answer. 00 Σ 6 + cos 3k ko k=1 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) OA. The series is a p-series with p= so the series converges by the properties of a p-series. 00 OB. The Integral Test yields J f(x) dx = .so the series diverges by the Integral Test. 0 6 + cos 3k O...
Determine whether the series converges or diverges (show your answers in detail). -5k 2 + k = 1
Determine whether the following series converges. Justify your answer. 00 5 Σ KE1 (k+4)* 6 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The series is a geometric series with common ratio so the series converges by the properties of a geometric series. OB. The series is a p-series with p = so the series converges by the properties of a p-series. OC. The limit of the...
Determine whether the following series converges. Justify your answer. 8 + cos 10k Σ k= 1 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) 8+ cos 10k 9 O A. Because 9 E and, for any positive integer k, E converges, the given series converges by the Comparison Test. 8 k=1 00 OB. The Integral Test yields f(x) dx = so the series diverges by the Integral...
10.4.16 Use the Divergence Test to determine whether the following series diverges 249 Σ k= 1 Choose the correct answer below. O A. The series diverges because lim k-00 2k9 k! = 0. B. The series converges because lim K00 2K K! 0. OC. The series converges because lim K+00 2kº -0. D. The series diverges because lim 2k k! *0 00 The mai
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Determine whether the following series converges. Justify your answer. 00 14 k พ 14k k= 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The series is a geometric series with common ratio so the series converges by the properties of a geometric series. B. The Root Test yields p = so the series diverges by the Root Test. C. The Ratio Test...
Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 00 k-1 k= 1 Select the correct choice below and fill in any answer boxes within your choice. O A. The series converges. The sum of the series is (Type an integer or a simplified fraction) B. The series diverges.
00 Determine whether the series 2" +5" 6 converges or diverges. If it converges, find its sum. n=1 Select the correct answer below and, if necessary, fill in the answer box within your choice. O A. The series diverges because it is the sum of two geometric series, at least one with In 21. The series converges because it is the sum of two geometric series, each with (r< 1. The sum of the series is OB (Simplify your answer.)...
Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 00 k=1 Select the correct choice below and fill in any answer boxes within your choice. O A. The series converges. The sum of the series is (Type an integer or a simplified fraction.) OB. The series diverges.