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Please show the step-by-step solution. Thanks!
Use the Ratio Test to determine the values of x...
Determine whether the following series converges. Select the correct choice below and, if necessary, fill in...
Determine whether the following series converges. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. Because -, for any positive integer k, and 2Ink + 2 diverges, the series diverges by the Comparison Test. +2 k+2 OB. Since J - = 0o, the series diverges by the Integral Test. Ink + 2 8 c. Because Ink +2 —, for any positive integer k, and converges, the...
Use the Ratio Test to determine whether the series converges ab 00 2k Σ k 149...
Use the Ratio Test to determine whether the series converges ab 00 2k Σ k 149 k= 1 Select the correct choice below and fill in the answer box to compl (Type an exact answer in simplified form.) O A. The series converges absolutely because r = OB. The series diverges because r= O c. The Ratio Test is inconclusive because r=
please show all steps Use the Integral Test to determine the convergence or divergence of the...
please show all steps
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. 2 Σ k(Ink)? k= 3 Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. 2. The series converges. The value of the integralſ dx is x(In x)2 (Type an exact answer.) B. 2 The series diverges. The value of the integralſ -dx is x(...
please show all work.. Determine whether the following series converges. Justify your answer. 00 14 k...
please show all work..
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...
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. 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...
Use the Integral Test to determine the convergence or divergence of the following series, or state...
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. 1 5e 2k k=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. dx The series converges. The value of the integralſ is 5 e 2x 3 (Type an exact answer.) OB. dx The series diverges. The value of the integral is 5 e 2x (Type an exact answer.)...
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.
Use the integral Test to determine the convergence or divergence of the following series, or state...
Use the integral Test to determine the convergence or divergence of the following series, or state that the conditions of the test are not satisfied and therefore 2 ke- Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. Since the integral dx converges to the series also converges. (Type an exact answer.) OB. Since the integral xe ** dx diverges, the series also diverges O c. The Integral Test does...
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...
Determine whether the following series converges. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. Because -, for any positive integer k, and 2Ink + 2 diverges, the series diverges by the Comparison Test. +2 k+2 OB. Since J - = 0o, the series diverges by the Integral Test. Ink + 2 8 c. Because Ink +2 —, for any positive integer k, and converges, the...
Use the Ratio Test to determine whether the series converges ab 00 2k Σ k 149 k= 1 Select the correct choice below and fill in the answer box to compl (Type an exact answer in simplified form.) O A. The series converges absolutely because r = OB. The series diverges because r= O c. The Ratio Test is inconclusive because r=
please show all steps
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. 2 Σ k(Ink)? k= 3 Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. 2. The series converges. The value of the integralſ dx is x(In x)2 (Type an exact answer.) B. 2 The series diverges. The value of the integralſ -dx is x(...
please show all work..
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...
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. 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...
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. 1 5e 2k k=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. dx The series converges. The value of the integralſ is 5 e 2x 3 (Type an exact answer.) OB. dx The series diverges. The value of the integral is 5 e 2x (Type an exact answer.)...
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.
Use the integral Test to determine the convergence or divergence of the following series, or state that the conditions of the test are not satisfied and therefore 2 ke- Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. Since the integral dx converges to the series also converges. (Type an exact answer.) OB. Since the integral xe ** dx diverges, the series also diverges O c. The Integral Test does...
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...
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