Find the interval of convergence of (x^n)/(n +1)

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Homework Help Overview

The discussion revolves around finding the interval of convergence for the series represented by (x^n)/(n + 1). Participants are exploring the application of the ratio test in this context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the ratio test but expresses uncertainty about progressing from the limit they derived. They question whether it is safe to assume the interval of convergence is from -∞ to ∞ based on their limit evaluation.

Discussion Status

Some participants emphasize the importance of not making assumptions without proof, prompting further inquiry into the original poster's understanding of factorials and their role in the problem.

Contextual Notes

The original poster indicates difficulty in dealing with factorials, which may be impacting their ability to apply the ratio test effectively.

Painguy
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Homework Statement


My main issue here is that if I use the ratio test I end up with lim (x(n!+1))/((n+1)!+1) n-> ∞

I don't know how to progress here. I believe that the limit will equal 0 and so it's interval of convergence is from -∞<x<∞ with a Radius of convergence of ∞. Is it safe for me to assume that?

Homework Equations





The Attempt at a Solution

 
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It is never safe to assume anything. Prove it.

ehild
 
ehild said:
It is never safe to assume anything. Prove it.

ehild

Well that's why I was asking. I'm not sure how to deal with the factorials here.
 
Well, do you know what n! is?

ehild
 

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