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

• srfriggen
In summary, the series 1/2n is divergent. This can be shown using the integral test, which the person is familiar with but has not covered in class yet. Another approach is to compare it to the harmonic series, which has been shown to be divergent. The argument of 1/2 * 1/n = 1/2 x divergent = D also makes sense, but it would be more elegant to use a theorem or justification. However, since the question only asks for convergence or divergence, this information may not be necessary.

#### srfriggen

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.

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. :)