Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let R, = S-S, be the remainder in approximating the value of that series by the sum of k=1 its first n terms. Then R,san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series (-1)% -, evaluate the nth partial sum for n=2. Then find an upper bound for the error s-S, in using the nth partial sum S, to estimate the value of the series S. 00 k=0 (6k + 1)*
Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let R, = S-S, be the remainder in approximating the value of that series by the sum of k=1 its first n terms. Then R,san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series (-1)% -, evaluate the nth partial sum for n=2. Then find an upper bound for the error s-S, in using the nth partial sum S, to estimate the value of the series S. 00 k=0 (6k + 1)*
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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I understand how to find the nth partial sum for n=2. But the second part of finding the upper bound for the error isn't working out for me. Can you explain clearly how to do that? I thought I just took n=2+1 or n=3 and then used that value for k, but the system says that's not the right answer.
Transcribed Image Text:Let 2 (-1)**'ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let R, = S-S, be the remainder in approximating the value of that series by the sum of
k=1
its first n terms. Then R,san+ 1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series
(-1)%
-, evaluate the nth partial sum for n=2. Then find an upper bound for the error s-S, in using the nth partial sum S, to estimate the value of the series S.
00
k=0 (6k + 1)
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