Assuming that the triangle inequality |a + b| |a| + |b| holds for any two numbers

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Assuming that the triangle inequality |a + b| ≤ |a| + |b| holds for any two numbers a and b, show that

for any n numbers.

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Related Book For answer-question

Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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Question Posted: May 11, 2023 03:13 AM

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Assuming that the triangle inequality |a + b| |a| + |b| holds for any two numbers

Question:

|x₁ + x₂ + + x₂| = |x₁| + |x₂| ++ xn

Step by Step Answer:

We can prove this statement by using mathematical induction Base case When n 2 we have a1 a2 a3 a1 a...View the full answer

Thomas Calculus Early Transcendentals

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