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(-1)* Consider the series (2k)! k=0 (-1)* to within 10-5 of the actual sum of the series. (You may assume (a) Determine n so that s, 2 (2k)! k=0 that this series converges by the Alternating Series Test.) Note: 0! = 1. (b) Compute Sn using the n you found in part (a). Round your answer to 8 decimal places. (c) The actual sum of the series is cos(1) (in radians). What is the actual error in this case? Give your answer to 8 decimal places.

(-1)* Consider the series (2k)! k=0 (-1)* to within 10-5 of the actual sum of the series. (You may assume (a) Determine n so that s, 2 (2k)! k=0 that this series converges by the Alternating Series Test.) Note: 0! = 1. (b) Compute Sn using the n you found in part (a). Round your answer to 8 decimal places. (c) The actual sum of the series is cos(1) (in radians). What is the actual error in this case? Give your answer to 8 decimal places.

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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1. Consider the series \(\sum_{k=0}^{\infty} \frac{(-1)^k}{(2k)!}\). (a) Determine \(n\) so that \(s_n \approx \sum_{k=0}^{\infty} \frac{(-1)^k}{(2k)!}\) to within \(10^{-5}\) of the actual sum of the series. (You may assume that this series converges by the Alternating Series Test.) Note: \(0! = 1\). (b) Compute \(s_n\) using the \(n\) you found in part (a). Round your answer to 8 decimal places. (c) The actual sum of the series is \(\cos(1)\) (in radians). What is the actual error in this case? Give your answer to 8 decimal places.
Transcribed Image Text:1. Consider the series \(\sum_{k=0}^{\infty} \frac{(-1)^k}{(2k)!}\). (a) Determine \(n\) so that \(s_n \approx \sum_{k=0}^{\infty} \frac{(-1)^k}{(2k)!}\) to within \(10^{-5}\) of the actual sum of the series. (You may assume that this series converges by the Alternating Series Test.) Note: \(0! = 1\). (b) Compute \(s_n\) using the \(n\) you found in part (a). Round your answer to 8 decimal places. (c) The actual sum of the series is \(\cos(1)\) (in radians). What is the actual error in this case? Give your answer to 8 decimal places.
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