1. (Alternating Series Test.) This shows that for this particular sort of alternating series, the error...
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....
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?
(Exercise 4.13, reordered) Given a series ΣΧί ak, let 8,-Ση-i ak. Σχί ak is Cesaro summable if S1 + 82 +... +Sn lim n-+o converges. (a) Give an example of a series Σ00i ak that is Cesaro sum mable but not convergent (b) Prove that if 1 ak converges, then it is Cèsaro summable. Hint: Say the sequence of partial sums sn → L. Try to prove that =1 8k → L by showing and then splitting the latter sum...
The Alternating Series Test and convergence. 8 = angle Pod sino g 3! as 3! a 7 " Functions can often be represented by an infinite series. A series reprezentation can help to solve differential equations, to fin derivatives, or to compute integrals involving the function. Computers also use these series representations to perform calculations. For example sin (0) 0 +... allows a calculator to give a decimal approximation of values of sine. Click here to access the Exo ore...
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It 2n=1 have to check that - trust me on this one.) (2n+1) (a) Use a calculator to evaluate the partial sum S3 of this series. Give the answer rounded to four decimal places. (b) Estimate the error of using S3 as an approximation to the sum of the series, i.e. estimate the remainder R3. Recall that the remainder estimate of the Alternating Series Test...
(1 point) The series is an alternating series but we can apply the ratio test to to test for absolute convergence. Applying the ratio test for absolute convergence you would compute lim (k+1 = li k00 ak k- 00 Hence the series converges Note that you will have to simplify your answer for the limit or you will get an error message.
a,b,c and d (-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
Please answer all parts. (1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
Use the alternating series test to prove that P (-1)" 2ºn2 - converges. n!
Find the Nth partial sum of the infinite series and evaluate its limit to determine whether the series converges or diverges. 00 1 n+ 5 1 n + 6 n = 1 Sn = converges diverges If the series is convergent, find its sum. (If an answer does not exist, enter DNE.) 1/6 Need Help? Read It Watch It Talk to a Tutor Find the Nth partial sum of the infinite series and evaluate its limit to determine whether the...