Calculus 2 interval of convergence -- checking end points

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Homework Help Overview

The discussion revolves around determining the interval of convergence for a series in a calculus context, specifically focusing on the convergence or divergence of the endpoints of that interval.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the correct test for the endpoints after identifying the interval of convergence. They express difficulty in selecting the appropriate method for this verification.
  • Some participants question the clarity of the original poster's work due to the use of an unreadable image, suggesting that the information be typed out for better understanding.
  • Another participant notes that if the variable x is negative, it may indicate the presence of an alternating series.

Discussion Status

The discussion is ongoing, with participants providing feedback on the clarity of the original poster's submissions and suggesting that they clarify their work. There is an acknowledgment of the need for further exploration of the convergence tests applicable to the endpoints.

Contextual Notes

There are constraints regarding the readability of submitted images, which may hinder effective communication of the problem details. The original poster has attempted to share links to images for reference.

rossmoesis
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Homework Statement


[PLAIN]http://email.photobucket.com/wf/click?upn=tRCgAMfEfk8moxY0TjPC4lPPM0sXOKwutyIq47CMTKs0dzyywVYzTaMWH8-2Bzo5-2FsAT1hSn2u8nhtTlXRVI-2BDs3dbLwqV7FVPJZdCfwS6qDorV0c-2Blq6XRnrVUYsLffi2id9Ma4XDGYssMtivke9T0A-3D-3D_whPbjyDNqQqG-2FABCOAcFDhlciHlWVosDuzGNcx8ulLn1XPsw3RItB9a0ZKzbWUjhD5QN0BjKqPT3p-2FFMYnHwCHkxJ8U7UgTdccAw-2BQNDt-2FWYcVOcGYWyPrDnhFZ4wxeKwtHSMH-2FU0Ev-2FD82L-2F5FVMYpPr42BkMfKA0c7B9UFHMZbfml3RpIMxX73T-2BjugVi6TYP6-2BFgjtfKZemv5vG8xCDZrA74p9b7HQm1E0kHNLeQDGCyjMm4HzzVR9GA23nwt
http://email.photobucket.com/wf/click?upn=tRCgAMfEfk8moxY0TjPC4lPPM0sXOKwutyIq47CMTKs0dzyywVYzTaMWH8-2Bzo5-2FsAT1hSn2u8nhtTlXRVI-2BDs3dbLwqV7FVPJZdCfwS6qDorV0c-2Blq6XRnrVUYsLffi2id9Ma4XDGYssMtivke9T0A-3D-3D_whPbjyDNqQqG-2FABCOAcFDhlciHlWVosDuzGNcx8ulLn1XPsw3RItB9a0ZKzbWUjhD5QN0BjKqPT3p-2FFMYnHwCHkxJ8U7UgTdccAw-2BQNDt-2FWYcVOcGYWyPrDnhFZ4wxeKwtHSMH-2FU0Ev-2FD82L-2F5FVMYpPr42BkMfKA0c7B9UFHMZbfml3RpIMxX73T-2BjugVi6TYP6-2BFgjtfKZemv5vG8xCDZrA74p9b7HQm1E0kHNLeQDGCyjMm4HzzVR9GA23nwt

Homework Equations



Ratio test

The Attempt at a Solution



I found the interval of convergence. I'm having a hard time finding the correct test to make sure my end points either converge or diverge. I attached a picture of my work. Some hints would be greatly appreciated.
 
Last edited by a moderator:
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rossmoesis said:

Homework Statement


http://email.photobucket.com/wf/click?upn=tRCgAMfEfk8moxY0TjPC4lPPM0sXOKwutyIq47CMTKs0dzyywVYzTaMWH8-2Bzo5-2FsAT1hSn2u8nhtTlXRVI-2BDs3dbLwqV7FVPJZdCfwS6qDorV0c-2Blq6XRnrVUYsLffi2id9Ma4XDGYssMtivke9T0A-3D-3D_whPbjyDNqQqG-2FABCOAcFDhlciHlWVosDuzGNcx8ulLn1XPsw3RItB9a0ZKzbWUjhD5QN0BjKqPT3p-2FFMYnHwCHkxJ8U7UgTdccAw-2BQNDt-2FWYcVOcGYWyPrDnhFZ4wxeKwtHSMH-2FU0Ev-2FD82L-2F5FVMYpPr42BkMfKA0c7B9UFHMZbfml3RpIMxX73T-2BjugVi6TYP6-2BFgjtfKZemv5vG8xCDZrA74p9b7HQm1E0kHNLeQDGCyjMm4HzzVR9GA23nwt
http://email.photobucket.com/wf/click?upn=tRCgAMfEfk8moxY0TjPC4lPPM0sXOKwutyIq47CMTKs0dzyywVYzTaMWH8-2Bzo5-2FsAT1hSn2u8nhtTlXRVI-2BDs3dbLwqV7FVPJZdCfwS6qDorV0c-2Blq6XRnrVUYsLffi2id9Ma4XDGYssMtivke9T0A-3D-3D_whPbjyDNqQqG-2FABCOAcFDhlciHlWVosDuzGNcx8ulLn1XPsw3RItB9a0ZKzbWUjhD5QN0BjKqPT3p-2FFMYnHwCHkxJ8U7UgTdccAw-2BQNDt-2FWYcVOcGYWyPrDnhFZ4wxeKwtHSMH-2FU0Ev-2FD82L-2F5FVMYpPr42BkMfKA0c7B9UFHMZbfml3RpIMxX73T-2BjugVi6TYP6-2BFgjtfKZemv5vG8xCDZrA74p9b7HQm1E0kHNLeQDGCyjMm4HzzVR9GA23nwt

Homework Equations



Ratio test

The Attempt at a Solution



I found the interval of convergence. I'm having a hard time finding the correct test to make sure my end points either converge or diverge. I attached a picture of my work. Some hints would be greatly appreciated.

Your photo is unreadable on my screen. Please type it all out (as per PF standards), but if you still insist on posting an image, at least work at making it usable.
 
Last edited by a moderator:
Ray Vickson said:
Your photo is unreadable on my screen. Please type it all out (as per PF standards), but if you still insist on posting an image, at least work at making it usable.

I tried to go back and edit the post but was unable to. This link should work for the problem

http://s30.postimg.org/k3ksocech/scan.jpg

thanks for the heads up.
 
rossmoesis said:
I tried to go back and edit the post but was unable to. This link should work for the problem

http://s30.postimg.org/k3ksocech/scan.jpg

thanks for the heads up.

If x is negative, then you have an alternating series.