Ask your own question, for FREE!
Mathematics 15 Online
OpenStudy (anonymous):

does sum (1 to inf) of tan (1/n) converges or diverges?

OpenStudy (anonymous):

Oh, sorry, I'm getting ahead of myself. That test doesn't help...

OpenStudy (anonymous):

Yes, I know. I was planning on using the test for divergence, which involves a limit. But it doesn't work for this series.

OpenStudy (anonymous):

it goes to 0 that makes it inconclusive

OpenStudy (anonymous):

I'm thinking comparison test. For sufficiently large n, you have \(\large\tan\left(\frac{1}{n}\right)\le\frac{1}{n}.\) Let me verify that...

OpenStudy (anonymous):

hmm i tried that but it didn't seem to work or rather i tries \(\tan(\frac{1}{n})>\frac{1}{n}\) to show it diverges, but that does not work

OpenStudy (anonymous):

oh wait, maybe it will work!

OpenStudy (anonymous):

What about \(\large\frac{2}{n}\)?

OpenStudy (anonymous):

i think they are the same

OpenStudy (anonymous):

constant does not play role in comparison test generally so its same

OpenStudy (anonymous):

i mean i think \[\tan(\frac{1}{n})\sim\frac{1}{n}\]

OpenStudy (anonymous):

i think can check that \[\lim_{n\to \infty}\frac{\tan(\frac{1}{n})}{\frac{1}{n}}=1\]

OpenStudy (anonymous):

Yeah, I was just checking that myself. It's correct.

OpenStudy (anonymous):

l'hopital gets it in one step i believe

OpenStudy (anonymous):

And wolfram also says that the series diverges by comparison test: http://www.wolframalpha.com/input/?i=series+tan%281%2Fn%29+from+n%3D1+to+infinity

OpenStudy (anonymous):

whew!

OpenStudy (anonymous):

try l'hopital, it will give the limit as 1, so diverges by comparison

OpenStudy (anonymous):

guys, in that case limit = 1, when limit = 1, test is inconclusive again

OpenStudy (anonymous):

in ratio test, if limit < 1, it converge, limit > 1 , it diverge and limit= 1 , its inconclusive

OpenStudy (anonymous):

@satellite73

OpenStudy (anonymous):

Limit comparison test, not ratio test.

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos: Ah trying out the whole T.V girl drawing :p (I love drawing eyes)
5 minutes ago 8 Replies 5 Medals
kaelynw: starting to draw a hand
1 day ago 16 Replies 2 Medals
Twaylor: Rate it :D (Took 2 days)
2 days ago 7 Replies 0 Medals
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
3 hours ago 7 Replies 1 Medal
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
3 days ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
3 days ago 27 Replies 3 Medals
kaelynw: art igg
3 days ago 14 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!