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3. For all n E N prove that 1 e 0 < e – Σ k! k=0 (n + 1)! Hint: Think about Taylor approximations of the function e".

3. For all n E N prove that 1 e 0 < e – Σ k! k=0 (n + 1)! Hint: Think about Taylor approximations of the function e".

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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Taylor approximations 

3. For all n EN prove that 1 e 0 < e – Σ k! k=0 (n + 1)!" Hint: Think about Taylor approximations of the function e".
Transcribed Image Text:3. For all n EN prove that 1 e 0 < e – Σ k! k=0 (n + 1)!" Hint: Think about Taylor approximations of the function e".
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