Prove the inequality | x 1 + x 2 + ... + x n | ≤ | x 1 | + | x 2 | + ... + | x n | holds for any n numbers.

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Answer 1

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Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

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Answer 2

Question

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

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Answer 3

Question

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

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Answer 4

Question

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

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Answer 5

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

Answer 6

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

Answer 7

Chapter A.2, Problem 1E

To determine

Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. A.2 - Assuming that the triangle inequality holds for...Ch. A.2 - Show that if r ≠ 1, then for every positive...Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - Show that for all positive integers n. Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - Show that 2n ≥ 1/8 for n ≥ –3. Ch. A.2 - Sums of squares Show that the sum of the squares...Ch. A.2 - Sums of cubes Show that the sum of the cubes of...

Prove the inequality | x 1 + x 2 + ... + x n | ≤ | x 1 | + | x 2 | + ... + | x n | holds for any n numbers.

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Prove the inequality |x1+x2+...+xn|≤|x1|+|x2|+...+|xn| holds for any n numbers.

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Chapter A.2 Solutions