Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. Round to six decimal places. ∑ n = 1 ∞ (−1) n + 1 1 2 n A. 0.015625 B. 0.062500 C. 0.031250 D. 0.156250
Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. ∑ n = 1 ∞ (−1) n + 1 t n n, − 1 < t ≤ 1 |Error| < |t 4 4| |Error| < 0.20 |Error| < |t 5| |Error| < |t 5 5| |Error| < |t 3 3| |Error| < |t 4| |Error| < |t 3|
Consider the series ∑ n = 2 ∞ x n n(lnn) 10. (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally?
Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. ∑ n = 0 ∞ 1 n + 13 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The test is inconclusive because lim n → ∞ 1 n + 13 = ◻. B. The series diverges because lim n → ∞ 1 n + 13 exists and is equal to ◻. C. The series diverges because lim n → ∞ 1 n + 13 = − ∞ and fails to exist. D. The series diverges because lim n → ∞ 1 n + 13 = ∞ and fails to exist.
Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. ∑ n = 1 ∞ cos 11 n Choose the correct answer below. A. The test is inconclusive because lim n → ∞ cos 11 n = ◻. B. The series diverges because lim n → ∞ cos 11 n = ∞ and fails to exist. C. The series diverges because lim n → ∞ cos 11 n exists and is equal to ◻. D. The series diverges because lim n → ∞ cos 11 n = − ∞ and fails to exist.
Use the nth-term test for divergence to show that the series is divergent, or state that the test is inconclusive. ∑ n = 1 ∞ ln 1 n Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The series diverges because lim n → ∞ ln 1 n = − ∞ and fails to exist. B. The series diverges because lim n → ∞ ln 1 n exists and is equal to ◻. C. The series diverges because lim n → ∞ ln 1 n = ∞ and fails to exist. D. The test is inconclusive because lim n → ∞ ln 1 n = ◻.
Consider the following series. ∑ n = 1 ∞ (−1) n + 1 n 4 (∣error∣ < 0.00005) Show that the series is convergent. Since this series is -- Select--, which condition(s) below show that it converges? (Select all that apply.) lim n → ∞ 1 n 4 = 0 1 (n + 1) 4 < 1 n 4 1 (n + 1) 4 > 1 n 4 lim n → ∞ 1 (n + 1) 4 = 0 How many terms of the series do we need to add in order to find the sum to the indicated accuracy? terms
Consider the alternating series. ∑ n = 1 ∞ (−1) n + 1 n Given that the series converges, find the smallest integer k such that the kth partial sum, ∑ n = 1 k (−1) n + 1 n, estimates the series to within |0.01|.