For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: min (SN, SN+1) SSS max (SN, SN+1). 00 Consider S (-1)+1 7² Answer: and write S= N=1 (a) Find the smallest value of N for which the interval bracketing S in line (+) above has length at most 10- Answer: S (-1)+1 72³ (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (+). A spreadsheet may be helpful to calculate the sum Sy- SN+SN+1 2
For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: min (SN, SN+1) SSS max (SN, SN+1). 00 Consider S (-1)+1 7² Answer: and write S= N=1 (a) Find the smallest value of N for which the interval bracketing S in line (+) above has length at most 10- Answer: S (-1)+1 72³ (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (+). A spreadsheet may be helpful to calculate the sum Sy- SN+SN+1 2
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:For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums:
min (SN, SN+1) SSS max (SN, SN+1).
00
Consider S (-1)+1
7²
Answer:
and write S=
N=1
(a) Find the smallest value of N for which the interval bracketing S in line (+) above has length at most 10-
Answer: S
(-1)+1
12³
(b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (). A spreadsheet may be helpful to calculate the sum Sy-
SN+SN+1
2
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