Q: Is 1/2n Convergent or Divergent? Help Appreciated

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Homework Help Overview

The discussion revolves around the convergence or divergence of the series 1/2n. The original poster expresses uncertainty about how to prove whether the series converges or diverges, noting that the limit as n approaches infinity is zero but questioning its implications.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the potential use of the integral test and the harmonic series as a reference point for divergence. The original poster questions the validity of comparing the series to 1/n and explores the implications of multiplying a divergent series by a constant.

Discussion Status

The conversation is ongoing, with participants providing insights and questioning the original poster's reasoning. There is a recognition of the limitations of the original poster's current knowledge, and some guidance is offered regarding the relationship between divergent series and constants.

Contextual Notes

The original poster mentions that they have not yet covered certain topics in class, which may limit their ability to fully engage with the problem. There is also an acknowledgment of the challenges of discussing complex topics in an informal setting.

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Q: Is the series 1/2n convergent or divergent? If convergent find it's sum.

I see that the limit as n goes to infinity is zero but that does not prove C or D. It seems like it would be divergent but why? How can that be shown?

Any direction/help would be greatly appreciated.
 
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Try an integral test. Do you know that one?
 
Yes I do but I shouldn't lol (we haven't gotten to that in class). We have covered the harmonic series and shown it is D.

I also notice I can't do a comparison to 1/n since 1/n > 1/2n.
Would the argument 1/2 * 1/n = 1/2 x divergent = D make sense?
 
srfriggen said:
Yes I do but I shouldn't lol (we haven't gotten to that in class). We have covered the harmonic series and shown it is D.

I also notice I can't do a comparison to 1/n since 1/n > 1/2n.
Would the argument 1/2 * 1/n = 1/2 x divergent = D make sense?

Sure. If a series is divergent, then any nonzero constant times the series is also divergent. That's true. But do you have a theorem or something to justify it rather than just writing divergent*(1/2)=divergent? That just seems a little sloppy.
 
Yeah I know. I'm typing on this forum from my phone so it's tough to be elegant lol. The question only asks C or D but I kinda wanted to know for my own purposes but thanks for the help in understanding it. :)
 

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