(-1)* (2k)! 1. Consider the series k=0 Σ (-1)* (a) Determine n so that s, = to within 10-5 of the actual sum of the series. (You may assume (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)* (2k)! 1. Consider the series k=0 Σ (-1)* (a) Determine n so that s, = to within 10-5 of the actual sum of the series. (You may assume (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
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 was stuck on how to factor out the factorial when using remainder theorem for the questions below.
Transcribed Image Text:(-1)k
1. Consider the series
(2k)!
k=0
(-1)k
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.
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