Let Σ (-1)* ¹a be a convergent alternating series with terms that are nonincreasing in magnitude. Let R₁ = S-S₁, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R₁|san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first k=1 neglected term. For the convergent alternating series (1) -o (3k +113 evaluate the nth partial sum for n=2. Then find an upper bound for the error |S-Sn in using the nth partial sum S, to estimate the value of the series S. The nth partial sum for the given value of n is 0.984375 (Type an integer or a decimal. Round to seven decimal places as needed.) Using the provided theorem, the upper bound for the error is (Type an integer or a decimal. Round to seven decimal places as needed.)
Let Σ (-1)* ¹a be a convergent alternating series with terms that are nonincreasing in magnitude. Let R₁ = S-S₁, be the remainder in approximating the value of that series by the sum of its first n terms. Then |R₁|san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first k=1 neglected term. For the convergent alternating series (1) -o (3k +113 evaluate the nth partial sum for n=2. Then find an upper bound for the error |S-Sn in using the nth partial sum S, to estimate the value of the series S. The nth partial sum for the given value of n is 0.984375 (Type an integer or a decimal. Round to seven decimal places as needed.) Using the provided theorem, the upper bound for the error is (Type an integer or a decimal. Round to seven decimal places as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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