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z2n+1 7. Prove that sin z = (−1)”. converges absolutely for all z € C. Use (2n + 1)! n=0 this fact and Proposition 7 from the Week 5 Lecture Notes to conclude that ∞ z2n Σ(-1). also converges absolutely for all z E C. (2n)! COS 2 = n=0

z2n+1 7. Prove that sin z = (−1)”. converges absolutely for all z € C. Use (2n + 1)! n=0 this fact and Proposition 7 from the Week 5 Lecture Notes to conclude that ∞ z2n Σ(-1). also converges absolutely for all z E C. (2n)! COS 2 = n=0

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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z2n+1 7. Prove that sin z = (−1)”. converges absolutely for all z € C. Use (2n + 1)! n=0 this fact and Proposition 7 from the Week 5 Lecture Notes to conclude that ∞ z2n Σ(-1). also converges absolutely for all z E C. (2n)! COS 2 = n=0
Transcribed Image Text:z2n+1 7. Prove that sin z = (−1)”. converges absolutely for all z € C. Use (2n + 1)! n=0 this fact and Proposition 7 from the Week 5 Lecture Notes to conclude that ∞ z2n Σ(-1). also converges absolutely for all z E C. (2n)! COS 2 = n=0
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