Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 1.7, Problem 9P

Prove that an absolutely convergent series ∑ n = 1 ∞ a n an is convergent. Hint: Put b n = a n + | a n | .

Then the b_n are nonnegative, we have | b n | ≤ 2 | a n | a n d a n = b n − | a n | .

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Chapter 1.7, Problem 8P

Chapter 1.7, Problem 10P

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Mathematical Methods in the Physical Sciences

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Prove that an absolutely convergent series ∑ n = 1 ∞ a n an is convergent. Hint: Put b n = a n + | a n | . Then the b n are nonnegative, we have | b n | ≤ 2 | a n | a n d a n = b n − | a n | .

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