Does the Series Converge or Diverge? SUM(cos(npi)/n)

Does the Series Converge or Diverge? SUM(cos(npi)/n)

If you enjoyed this video please consider liking, sharing, and subscribing.

There are several ways that you can help support my channel:)

Thank you:)

[henriqueduartejalles]

Bro i am seeing your video 10 minutes before exam, you are a savior

[Hewhoyettoknowhimself]

That's a very elegant solution. I did integration (via maclaurin series) and end up doing more calculation for the same result (y)

[TheOskro]

It's juicy that by multiplying the coefficient of the harmonic series by just (-1)^n over n we get convergence. Great video as always, keep it up my man!

[ednasassistant]

Thank you so much! I was very confused the first time I saw this problem, but your explanation makes a lot of sense!

[beatrice]

thank you so much for that solution I couldn't figure out how to deal with this cos(npi)

[DK-ikxv]

can we say 1/n^2 is smaller than or equal to [abs value of (cos n pi / n)] then do a comparison test and say that since the "smaller" expression 1/n^2 converges— since it is a p series with p>1— then the other series converges as well.

[eulermed]

Great I had also a doubt about the cosine Sir, There's an open problem about the convergence of the following series by the way Σ1/(n³ sin²n) n=1 to infinity

[Dr.Cassio_Esteves]

I study math for fun and I think that testing if a series converges or diverges is kinda boring. What I would like to know is: will this subject be important in the future? Is it required for anything interesting?
Sorry any mistakes, my English is a work in progress.

[sumittete]

How can you show the series sin(n) /n is not absolutely convergent?

[lordburiev]

hey, i wonder why 1/n diverges but in cos(n)/n which will be 1/n diverges?

[TheJuicebox]

Is it true that this series converges conditionally?