Interval of Convergence: Is it an Interval of Convergence Question?

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Homework Help Overview

The discussion revolves around determining the interval of convergence for the function log(1 + 2x). Participants are exploring whether the problem is fundamentally about interval of convergence or if it involves a different type of reasoning related to convergence properties.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Some participants question the original poster's approach of directly solving log(1 + 2x) < 1, suggesting that it may be more of a logic problem related to the convergence of the series. Others propose finding the power series for log(1 + 2x) through substitution to determine the interval of convergence.

Discussion Status

The discussion is active, with participants providing different perspectives on the nature of the problem. Some guidance has been offered regarding the use of power series and substitution, while others emphasize the need for clarity on the problem's classification within calculus topics.

Contextual Notes

There is a mention of the appropriateness of the problem's placement in the forum, with some participants suggesting it belongs in a more advanced section due to its calculus nature. The original poster expresses uncertainty about the method to derive the new series through substitution.

TyErd
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Homework Statement



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The Attempt at a Solution



I'm not exactly sure how to do this question. Is it an interval of convergence question where i simply let log(1+2x) < 1 and solve for x??
 

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It's actually more of a logic problem. They told you log(1+x) converges for |x|<1. So what's the range of convergence of log(1+2x)? You are overthinking this by quite a bit.
 
TyErd said:

Homework Statement



I've attached the question

Homework Equations





The Attempt at a Solution



I'm not exactly sure how to do this question. Is it an interval of convergence question where i simply let log(1+2x) < 1 and solve for x??
No. What I would do is find the power series for log(1 + 2x), which is simply a matter of a substitution, and then determine the interval of convergence of the new series.

BTW, calculus-type problems like this should not be posted in the Precalc section.
 
Mark44 said:
No. What I would do is find the power series for log(1 + 2x), which is simply a matter of a substitution, and then determine the interval of convergence of the new series.

BTW, calculus-type problems like this should not be posted in the Precalc section.

I don't think it's even much of a precalc question. See my previous post.
 
Dick said:
I don't think it's even much of a precalc question. See my previous post.
I agree that it's not a difficult problem, but being about series and convergence, it seems a better place for it is in the Calculus & Beyond section.
 
Mark44 said:
I agree that it's not a difficult problem, but being about series and convergence, it seems a better place for it is in the Calculus & Beyond section.

Your choice, of course. But I don't think you need any convergence tests to answer the question. x is a number, 2x is a number.
 
so your saying the answer is simply |2x| < 1?
 
Mark44 said:
No. What I would do is find the power series for log(1 + 2x), which is simply a matter of a substitution, and then determine the interval of convergence of the new series.

BTW, calculus-type problems like this should not be posted in the Precalc section.

Okay I understand how to do interval of convergences but how would I get the new series through substitution?
 

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