(b) Σ(-1)n-1-¹ n4 n=1

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Problem 3. Approximate each series to within the error 0.005.
1
(a) Ž(−1)²-1. n³
n=1
Solution. We first notice that the series converges by Alternating Series Test. We
now calculate the following partial sums:
We have that
n
Sn
(3) Σ(-1--
n=1
|s85 86 85| = |a6|≈ 0.004629 < 0.005
Therefore, s $50.904 is within 0.005 of the true sum.
1 2
3
4
5
6
1 0.875 0.912... 0.896... 0.904... 0.899...
1
4°
n²
-
Transcribed Image Text:Problem 3. Approximate each series to within the error 0.005. 1 (a) Ž(−1)²-1. n³ n=1 Solution. We first notice that the series converges by Alternating Series Test. We now calculate the following partial sums: We have that n Sn (3) Σ(-1-- n=1 |s85 86 85| = |a6|≈ 0.004629 < 0.005 Therefore, s $50.904 is within 0.005 of the true sum. 1 2 3 4 5 6 1 0.875 0.912... 0.896... 0.904... 0.899... 1 4° n² -
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