Series Absolute Convergence Proof

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Homework Help Overview

The discussion revolves around proving the absolute convergence of a series given that two other series converge. The subject area is primarily focused on series convergence in mathematical analysis.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of inequalities related to the terms of the series, specifically referencing the inequality 2|ab| < a^2 + b^2. There is uncertainty about how to prove this inequality and its relevance to the problem.

Discussion Status

Some participants are attempting to engage with the mathematical reasoning required for the proof, while others express difficulty in understanding how to proceed. Suggestions have been made regarding alternative inequalities to consider.

Contextual Notes

There is an indication of confusion regarding the proof process, and participants are reflecting on their understanding of the necessary mathematical concepts. No explicit consensus has been reached on the approach to take.

harrietstowe
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Homework Statement


If \suman2 and \sumbn2 converge show that \sumanbn is absolutely convergent


Homework Equations





The Attempt at a Solution


I think I should do something with the statement 2ab\leq a^2 + b^2
 
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Yes, you should. Better yet, use 2|ab|<a^2+b^2. Can you prove that?
 
Hey sorry to return to this late but I am still pretty stuck on this. Dick, I don't think I know how to prove that
 
harrietstowe said:
Hey sorry to return to this late but I am still pretty stuck on this. Dick, I don't think I know how to prove that

Better late than never. Try using (|a|-|b|)^2>=0.
 

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