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Use the alternating series test to prove that P (-1)" 2ºn2 - converges. n!
1) Use the Alternating Series Test to determine if the series converges.
The series converges by the Alternating Series Test. Use Theorem 9.9: Error Bounds for Alternating Series to find how many terms give a partial sum, Sn, within 0.01 of the sum, S, of the series. -1 I n Theorem 9.9: Error Bounds for Alternating Series Let n = Σ Suppose that 0 < an+1 < an for all n and limn-too an-0. Then (- 1)i-lai be the nth partial sum of an alternating series and let S = lim Sn....
1. (Alternating Series Test.) This shows that for this particular sort of alternating series, the error in approximating the infinite sum by a partial sum is at most the first omitted term. Suppose that aj > a2 > a3 > ... > 0 and that limnyoo An = 0. Let sn = {k=1(-1)kak. (a) Prove that if n > m > 0 then |sn – Sm! < am+1. (b) Prove that 2-1(-1)kak converges and that, for all n > 0,...
Problem 4. (1 point) Which of the following series converges by the Alternating Series Test? sin(n) 7n2 00 (-7) 72 B. n1 no 00 C. (-1)"n2 + 7n 2n2 + 10 n1 00 O D. (-1)" 7/n - 3 O E. Both A and B.
Study: Ch. 5 5.2 #93-96, 5.5 280-285 The given series converges by Alternating Series Test. Use the estimate |RN| <bn+1 to find the least value of N that guarantees that the sum Sy differs from the infinite sum n n=1 by at most an error of 0.01. Answer (a) What is N? (b) What is Sy and what is the actual sum S of the series? (c) Is S - SN <0.01?
Use the alternating series test to determine whether the series converges or diverges. Do 1 problem. 2n 1) Σ-1)". 2) Σ-1)" 3) Σ-1)**1. 4) 4η + 3 8 + 1η 4n' +2 cos(ηπ) 1 5) Στο Hel
please help (b) Determine whether the alternating series converges or diverges by using the alternating series test: 2n 4n-3 n=1
12. [8 points) Use either the Alternating Series Test or the Test for Divergence to determine if the series converges or diverges. (-1)"+1 2n + 3 n=1
The serie (-1)*+1 2. converges by Alternating Series Test. What is the smallest number of terms required to approximate the sum of the series with e < 10-4? none of the above 2n +1 Consider the series - n3 + 3n n=0 Which of the following statements are true? Check all that apply. 21 TL non The series is comparable to a geometric series. Root Test will work to establish convergence/divergence of the series. The series converges.
(1 point) Which of the following series converges by the Alternating Series Test? A. (-5)" n7 n1 B sin(n) 5n2 00 O C. (-1)"n2 +5n 3n2 + 7 n1 IM8 M8 00 D. n1 (-1)" 5n-1 E. Both A and B.