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Convergence question

  • Thread starter srfriggen
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  • #1
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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.
 

Answers and Replies

  • #2
Dick
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Try an integral test. Do you know that one?
 
  • #3
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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?
 
  • #4
Dick
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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.
 
  • #5
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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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