7T13 7m x-_ 뜨 11. (10 points) Suppose the infinite series n=1 4n-1+1 is approximated by...
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...
Due in 5 hours, 12 minutes, Due Mon 04/15/2019 11:5 Subtract the infinite series of In(1 -) from In(1 + z) to get a power series for Preview Evaluate this power series at z = to get 3 In(2)= Σ Preview What is the smallest N such that the Nth partial sum of this series approximates ln(2) with an error less than 0.001? Number of terms needed is: Points possible: 10 This Is attempt 1 of 3 Submit ービービーーーー1/1/1/10020000003-
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(a) Suppose an is an infinite series such that 0 < Ant1 < an for all n. Either give an argument that such a series always converges, or else explain why this is not the case (by a general argument or an example). n=1 (b) The nth derivative of the function In(1 + x) is (-1)"- (n − 1)! (1 + x)" Use the Taylor remainder theorem to show that the polynomial p(x) = x - 3x2 + 323 will...
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,...
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(1 point) Consider the following convergent series: Suppose that you want to approximate the value of this series by computing a partial sum, then bounding the error using the integral remainder estimate. In order to bound the value of the series between two numbers which are no more than 10 apart, what is the fewest number of terms of the series you would need? Fewest number of terms is 585 (1 point) Consider the following series: le(n Use...
Saved Required information The following infinite series can be used to approximate e =1+ z+ Use the Taylor series to estimate ) eat xi+11 for x- 0.25. Employ the zero-order, first-order, second-order, and third-order versions and compute the Et for each case. (Round the estimated values to five decimal places and the error values to one decimal place.) The calculated values are as follows: Value Order Error % Zero First Second Third
Saved Required information The following infinite series can...
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0. a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. c) When x=−2, for what values of p does the series converge? Explain your reasoning. (d) When p=1 and x=3.1, the series converges to a value SS....
Consider the following alternating series. (-1)*+ 1 3k k=1 (a) Show that the series satisfies the conditions of the Alternating Series Test. 1 3" Since lim o and an + 1 for all n, the series is convergent (b) How many terms must be added so the error in using the sum S, of the first n terms as an approximation to the sum n=10 X (c) Approximate the sum of the series so that the error is less than...
how to find the actual sum and how to find the maxinmum error,
do we have any formula? thanks
11 Let *(3n+1) Suppose we estimated Σ a" by computing the partial sum k-1-2+. According to the Alternating Series Estimation Theorem, (ak is an undenestimate, and the maximumerror is 12 (b) is an overestimate, and the maximum error is 24 (e) k is an overestimate, and the maximum error is 12 (d) The Alternating Series Estimation Theorem cannot be used because...
10.2 Series: Problem 5 Previous Problem Problem List Next Problem (1 point) Let s-Σ an be an infinite series such that SV-: 4-12 TL 1 10 16 (a) What are the values of Σ an and Σ an? n-4 10 16 n 4 (b) What is the value of as? a3 (c) Find a general formula for an TL (d) Find the sum an TL Note: You can earn partial credit on this problem Preview My Answers Submit Answers You...