1. Suppose you are told that the series 4, is a convergent alternating series with +ıl<«l...
8. If limy/ą. = L where L< 1, then the series Ža, is divergent. True False 10. A power series expansion for f(x) = 0._xj3 is f(x) = {xn-1. True False
ht2 univergent 4. For what values of is the following series convergent. lim lank & LI nas w I <! MA Find the sum in terms of .. divergent is - 3LX L3
1 1 Find the Taylor series for f(x) about <= 5. 3.2 4 The general term is an = The first five terms of the Taylor series are Show or upload your work below.
5) Suppose -1 an is a conditionally convergent series and let L E IR be arbitrary. Give an informal justification for each of the following. a. We can add up positive terms first, until the first time the sum is greater than L. Then we can add negative terms until the first time the resulting sum is less than L again. Moreover, we can always repeat this process. In repeating the process described in part a, at some point, each...
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...
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?
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,...
CODE IN JAVA to be typed in Eclipse The sum of the infinite series: f(r) = 1 + r + r4 r3+ is equal to 1/r), if Irl <1 Calculate the sum of the infinite series up to N terms and verify that the result is more accurate as we take more terms in the infinite series. For example, if r = 0.5, then the sum of the infinite series is 2. Check the value of f(r) when you take...
1. 2. (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...
I-x, 0 < x < 1 1 defined within 0 < x < 2 (note: L = 2) 1. (20pts) Consider the function f(x)- a) Write down the full sine series of f(x), as well as the partial sum of first 3 non-zero terms. b) Plot the odd periodic extension of nx) and the first non-zero term in the sine series, for-6 < er the function /(x)-x,0 6 (recall that L=2)