Determine whether the series (n-1)/(3n-1) is convergent or divergent.

Question

anonymous · Answer

$$\sum_{n=1}^{\infty}$$

zepdrix · Answer

I think you can easily show that it diverges by the ... Grrr i forget what all the tests are called lol.
The limit test?
The SEQUENCE isn't approaching 0 as n-> infinity, it's approaching 1/3. So as you add up those terms, you'll keep adding up 1/3 + 1/3 + 1/3.
No good :O

anonymous · Answer

it is converging, since as N gets bigger and biger, the answer becomes 1/3

anonymous · Answer

try for the answer n=100000, you will get a close number to 1/3. use l'hopital's rule.

zepdrix · Answer

The sequence doesn't converge to 0, meaning the series diverges. Am I remembering that correctly? :o

Every term in the series is approaching 1/3, so you won't get an answer around 1/3, you'll be ADDING UP a bunch of 1/3's.. which is definitely not convergent :o

anonymous · Answer

no, the series converges(goes to 1/3) diverge goes off to infinite.

anonymous · Answer

http://oxforddictionaries.com/definition/english/converge

zepdrix · Answer

Do you understand the difference between a sequence and a series jenxin? :o

anonymous · Answer

Ah, yes.  Since the limit doesn't equal 0 it is divergent.
Jenxin, you're thinking of a limit of a function of x, not a series

anonymous · Answer

ah okay. then yes, if it was a series, it would diverge to infinity, since as the more N's there are, it would be like 1/3 +1/3 + 1/3+ 1/3 to infinity.

anonymous · Answer

Well, thanks everyone.  I'm just getting lost in all of these rules lol

zepdrix · Answer

You're getting into power series now trevor? :D Ugh that's when math starts to suck a little bit lol.

anonymous · Answer

Yup!  So many different rules

anonymous · Answer

I love series. If you're a engineering major, you'll definitely need them later on

anonymous · Answer

I'm CS, so this is the kind of stuff I'll definitely need for Algorithms