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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let (-1)+1 ak 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
00
(-1)k
k=0 (3k+1)
evaluate the nth partial sum for n=2. Then find an upper bound for the error S-S₁ 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.)
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