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(a) Approximate the sum of the series by using the sum of the first 10 terms. Estimate the error involved in this approxima- tion. n=1 n³ (b) How many terms are required to ensure that the sum is accu- rate to within 0.0001?

(a) Approximate the sum of the series by using the sum of the first 10 terms. Estimate the error involved in this approxima- tion. n=1 n³ (b) How many terms are required to ensure that the sum is accu- rate to within 0.0001?

Advanced Engineering Mathematics
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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5. (a) Approximate the sum of the series 1 n³ n=1 the first 10 terms. Estimate the error involved in this approxima- tion. (b) How many terms are required to ensure that the sum is accu- rate to within 0.0001? by using the sum of ∞ 2 n 6. Determine whether the series Σ(−1)²+¹, n³ + 1 vergent, conditionally convergent, or divergent. n=1 is absolutely con-
Transcribed Image Text:5. (a) Approximate the sum of the series 1 n³ n=1 the first 10 terms. Estimate the error involved in this approxima- tion. (b) How many terms are required to ensure that the sum is accu- rate to within 0.0001? by using the sum of ∞ 2 n 6. Determine whether the series Σ(−1)²+¹, n³ + 1 vergent, conditionally convergent, or divergent. n=1 is absolutely con-
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