(a) Find the series’ radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. ∑ ∞ n=1 (-1)^n+1(x+11)^n/n11^n B. The series converges only at x = . (Type an integer or a simplified fraction.) C. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges absolutely for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x = . (Type an integer or a simplified fraction.) C. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges conditionally at x = . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There are no values of x for which the series converges conditionally.
(a) Find the series’ radius and interval of convergence. Find the values of x for which the series converges(b) absolutely and (c) conditionally. ∑ ∞ n=0 (x - 4)^n/6^n (a) The radius of convergence is . (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interval of convergence is . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges only at x = . (Type an integer or a simplified fraction.) C. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges absolutely for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x = . (Type an integer or a simplified fraction.) C. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges conditionally at x = . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There are no values of x for which the series converges conditionally.
(a) Find the series’ radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. ∑ ∞ n=1 (8x - 5)^2n+1 / n3/2 (a) The radius of convergence is . (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interval of convergence is . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges only at x = . (Type an integer or a simplified fraction.) C. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges absolutely for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x = . (Type an integer or a simplified fraction.) C. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges conditionally at x = . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There are no values of x for which the series converges conditionally.
(a) Find the series’ radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. ∑ ∞ n=0 √nx^n / 3^n (a) The radius of convergence is . (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interval of convergence is . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges only at x = . (Type an integer or a simplified fraction.) c. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges absolutely for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x = . (Type an integer or a simplified fraction.) C. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally for . (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges conditionally at x = . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There are no values of x for which the series converges conditionally.
Use an appropriate test to determine whether the series given below converges or diverges. Σ∞ k=1 tan 14/k Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The series converges because it is a geometric series with r = . B. The series converges per the Integral Test because R ∞ 1 tan 14 x dx = . C. The series diverges because the limit found in the nth Term Test is . D. The series converges because it is a p-series with p = . E. The Comparison Test with P 14 k shows that the series diverges. F. The Limit Comparison Test with P tan k shows that the series diverges.
Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ ∞ n=1 n!/3^n Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series diverges by the Absolute Convergence Test. B. The series diverges because the limit used in the nth-Term Test is . C. The series converges because the limit used in the nth-Term Test is . D. The Comparison Test with Σ∞ n=1 n! shows that the series diverges. E. The Comparison Test with Σ∞ n=1 1/3^n shows that the series converges. F. The series converges by the Absolute Convergence Test.
Use an appropriate test to determine whether the series given below converges or diverges. Σ∞ n=1 6n + 8/n(n + 1)(n + 2) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The series diverges because the limit used in the nthTerm Test is . (Type an exact answer.) B. The Comparison Test with Σ 6/n^2 shows that the series converges. C. The Comparison Test with Σ 6/n^2 shows that the series diverges.
Use the Root Test to determine if the series converges or diverges. Σ∞ k=1 (1 + 19/k)^k2 Select the correct choice below and fill in the answer box within your choice. (Type an exact answer in terms of e.) A. The series diverges because ρ = . B. The series converges because ρ = . C. The Root Test is inconclusive because ρ = .
Use an appropriate test to determine whether the series given below converges or diverges. Σ ∞ n=1 2n/7n - 6 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The series converges because the limit found in the nth-Term Test is . (Type an integer or a fraction.) B. The Comparison Test with Σ 1/n shows that the series converges. C. The Comparison Test with Σ n shows that the series diverges. D. The series diverges because the limit found in the nth-Term Test is . (Type an integer or a fraction.)
Use an appropriate test to determine whether the series given below converges or diverges. Σ ∞ n=1 2n/9n − 2 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The Comparison Test with Σ n shows that the series diverges. B. The series diverges because the limit found in the nth-Term Test is . (Type an integer or a fraction.) C. The Comparison Test with Σ 1/n shows that the series converges. D. The series converges because the limit found in the nth-Term Test is . (Type an integer or a fraction.)
Determine if the series to the right converges or diverges. Use any method, and give reasons for your answer. Σ∞ n=1 tan -1n n1.3 Choose the correct answer below. A. Since tan-1 n n1.3 < π/2 n1.3 for all n ≥ 1 and Σ∞ n=1 π/2 n1.3 converges, the given series converges by the comparison test. B. Since tan-1 n n1.3 < π/2 n for all n ≥ 1 and Σ∞ n=1 π/2 n diverges, the given series diverges by the comparison test. C. Since tan-1 n n1.3 < π/2 n1.3 for all n ≥ 1 and Σ∞ n=1 π/2 n1.3 diverges, the given series converges by the comparison test. D. Since tan-1 n n1.3 < π/2 n1.3 for all n ≥ 1 and Σ∞ n=1 π/2 n1.3 converges, the given series diverges by the comparison test.
Use an appropriate test to determine whether the series given below converges or diverges. Σ∞ k=1 1 √ k^3 - k + 1 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The Limit Comparison Test with Σ ∞ k=1 √ 1 k3 shows that the series converges. B. The series diverges per the Integral Test because ∫ ∞ 1 √ 1 k3-k+1 dx = . C. The series diverges because the limit found in the nth Term Test is . D. The series diverges because it is a p-series with p = . E. The series converges because it is a geometric series with r = . F. The Comparison Test with Σ∞ k=1 √ 1 k3 shows that the series converges.
Determine whether the series converges or diverges. Σ∞ n=1 n + 1/n^5 + n The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. Each term is less than that of a convergent p-series. The series diverges by the Limit Comparison Test. Each term is greater than that of a divergent p-series. The series diverges by the Limit Comparison Test. Each term is greater than that of a divergent geometric series.
Find out whether the series given below converges or diverges. Σ∞ n=1 8n + 1/n(n + 1)(n + 2) Choose the correct answer below. A. The comparison test with Σ 8/n^2 shows that the series converges. B. The comparison test with Σ 8/n^2 shows that the series diverges. C. The nth-term test shows that the series diverges.
Find out whether the series given below converges or diverges. Σ∞ n=1 1 n√n n Choose the correct answer below. A. The limit comparison test with Σ 1/n shows that the series diverges. B. The limit comparison test with Σ 1/n shows that the series converges. C. The nth-term test shows that the series converges.
Find out whether the series given below converges or diverges. Σ∞ n=1 1/5n + 4√n Choose the correct answer below. A. The limit comparison test with 1/√n shows that the series diverges. B. The limit comparison test with 1/4√n shows that the series diverges. C. The limit comparison test with 1/√n shows that the series converges. D. The limit comparison test with 1/4√n shows that the series converges.
Use an appropriate test to determine whether the series given below converges or diverges. Σ ∞ n=1 8n + 9/n(n + 1)(n + 2) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The Comparison Test with Σ 8/n^2 shows that the series converges. B. The Comparison Test with Σ 8/n^2 shows that the series diverges. C. The series diverges because the limit used in the nth-Term Test is . (Type an exact answer.)
Find out whether the series given below converges or diverges. Σ∞ n=3 1/n√n^2 - 5 Choose the correct answer below. A. The comparison test with Σ 1/n shows that the series diverges. B. The comparison test with Σ 1/n^3/2 shows that the series diverges. C. The comparison test with Σ 1/n shows that the series converges. D. The comparison test with Σ 1/n^3/2 shows that the series converges.