1. Prove the following results using the definition of |- and the triangle inequality. For n N and 9₁, 92,..., Un ER, 31 +32+...+yn|≤|y1| + |32|+ .+|ynl. Hint. Use induction.
1. Prove the following results using the definition of |- and the triangle inequality. For n N and 9₁, 92,..., Un ER, 31 +32+...+yn|≤|y1| + |32|+ .+|ynl. Hint. Use induction.
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. Prove the following results using the definition of || and the triangle
inequality.
For n N and y₁, 92,..., yn ER,
|y₁ + y2 +...+yn| ≤|y1| + |y2| + ... + |yn|.
Hint. Use induction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F544a9f38-3e68-4113-87a7-993914a696cb%2F35147c2a-787b-43e1-9d21-028dda9bc331%2F46wgbxe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Prove the following results using the definition of || and the triangle
inequality.
For n N and y₁, 92,..., yn ER,
|y₁ + y2 +...+yn| ≤|y1| + |y2| + ... + |yn|.
Hint. Use induction.
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