Rudin's principles of mathematical analysis

In summary, the conversation revolved around finding an expression for the Nth partial sum of a "telescoping series" and discussing the difficulties of evaluating it using the ratio or root test. The question of whether anyone had the book was also brought up.
  • #1
ehrenfest
2,020
1

Homework Statement


Does anyone have this book? I have some questions about chapter 3.

Homework Equations


The Attempt at a Solution

 
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  • #2
Try to find an expression for the Nth partial sum.

This is an example of what is called a "telescoping series".
 
  • #3
quasar987 said:
Try to find an expression for the Nth partial sum.

This is an example of what is called a "telescoping series".

Yes I figured that out before you posted and deleted that part of the post because it was embarrassing.

What about [itex]\sum_n \frac{\sqrt{n+1}-\sqrt{n}}{n} [/itex]. This definitely does not telescope. But both 1/n and \sqrt{n+1}-\sqrt{n} diverge so it is pretty clear that their product will. But what test should I use? The ratio test is too hard too evaluate. The root test is even harder to evaluate. What series can I compare it to?
 
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  • #4
ehrenfest said:
What about [itex]\sum_n \frac{\sqrt{n+1}-\sqrt{n}}{n} [/itex]

Hmm, is any term in that series larger than:
[tex]\frac{1}{2n^{\frac{3}{2}}}[/tex]

(This falls out easily with a little algebra.)
 
  • #5
NateTG said:
Hmm, is any term in that series larger than:
[tex]\frac{1}{2n^{\frac{3}{2}}}[/tex]

No (but I am not sure why you have the 2 there).

So, does anyone have the book?
 

1. What is "Rudin's principles of mathematical analysis"?

"Rudin's principles of mathematical analysis" is a widely used textbook written by Walter Rudin that covers the fundamental concepts and techniques in mathematical analysis, including real and complex analysis, measure theory, and functional analysis.

2. Who is "Rudin's principles of mathematical analysis" intended for?

This textbook is typically used by undergraduate and graduate students in mathematics, as well as by professionals in the field who are looking for a comprehensive and rigorous treatment of mathematical analysis.

3. What makes "Rudin's principles of mathematical analysis" stand out from other textbooks on the subject?

Rudin's textbook is known for its concise and clear writing style, as well as its rigorous and comprehensive approach to the subject. It also includes a wide range of challenging exercises and problems to help readers deepen their understanding of the material.

4. Is it necessary to have a strong background in mathematics to understand "Rudin's principles of mathematical analysis"?

While some familiarity with basic mathematical concepts is helpful, Rudin's textbook is designed to be accessible to students who are just beginning their study of mathematical analysis. It starts with the fundamentals and gradually builds upon them, making it suitable for both beginners and more advanced readers.

5. Are there any supplementary materials available for "Rudin's principles of mathematical analysis"?

Yes, there are many resources available to supplement the textbook, including solution manuals, study guides, and online lectures and tutorials. These can be found through various online platforms and through the publisher's website.

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