Homework Answers
The ratio test states that:
- if L < 1 then the series converges absolutely;
- if L > 1 then the series is divergent;
- if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.
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Use the Ratio Test to determine whether the series converges ab 00 2k Σ k 149...
Use the Ratio Test to determine if the series converges. 2K Lk kan k^ Select the...
Use the Ratio Test to determine if the series converges. 2K Lk kan k^ Select the correct choice below and fill in the answer box to complete your choice. O A. The series converges because r= . OB. The series diverges because r= . OC. The Ratio Test is inconclusive because r= 1.
Determine whether the following series converges absolutely, converges conditionally, or diverges. 00 (-1)+1e 3k Σ-11: -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...
Use the Divergence Test to determine whether the following series diverges or state that the test...
Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. n=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 lima ko (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim aka (Simplify your answer.) OC. The Divergence Test is inconclusive because lima. (Sirrplify your answer.) OD. The Divergence...
Determine whether the following series converges. Justify your answer. 00 5 Σ KE1 (k+4)* 6 Select...
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...
Use the Divergence Test to determine whether the following series diverges or state that the test...
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...
Determine whether the following series converges. 00 Σ 6-1 *2k/ Ink) Leta 20 represent the magnitude...
Determine whether the following series converges. 00 Σ 6-1 *2k/ Ink) Leta 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. The series converges because ak 6 k(Ink) Is nonincreasing in magnitude for k greater than some Index N and lim ax - k-00 and for any index N, there are some values of k> N for which ak +12 a, and some...
Determine whether the following series converges. Justify your answer. Σ 2 (k+5)3 k= 1 Select the...
Determine whether the following series converges. Justify your answer. Σ 2 (k+5)3 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 p-series with p= so the series converges by the properties of a p-series. OB. The series is a geometric series with common ratio so the series converges by the properties of a geometric series. OC. The series is a p-series with...
Determine whether the following series converges. Justify your answer. 00 Σ 6 + cos 3k ko...
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 following series converges. Justify your answer. 8 + cos 10k Σ k= 1...
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...
Use the Divergence Test to determine whether the following series diverges or state that the test...
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...
Use the Ratio Test to determine if the series converges. 2K Lk kan k^ Select the correct choice below and fill in the answer box to complete your choice. O A. The series converges because r= . OB. The series diverges because r= . OC. The Ratio Test is inconclusive because r= 1.
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...
Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. n=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 lima ko (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim aka (Simplify your answer.) OC. The Divergence Test is inconclusive because lima. (Sirrplify your answer.) OD. The Divergence...
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...
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...
Determine whether the following series converges. 00 Σ 6-1 *2k/ Ink) Leta 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. The series converges because ak 6 k(Ink) Is nonincreasing in magnitude for k greater than some Index N and lim ax - k-00 and for any index N, there are some values of k> N for which ak +12 a, and some...
Determine whether the following series converges. Justify your answer. Σ 2 (k+5)3 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 p-series with p= so the series converges by the properties of a p-series. OB. The series is a geometric series with common ratio so the series converges by the properties of a geometric series. OC. The series is a p-series with...
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 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...
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...
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