Question

I have tried investigate the convergence/divergence of the following question, yet ended up with having it converging when it's supposed to converge:
an = (-1)^n . (n+2)/(3n-1)

Answer 1

diverge*

Answer 2

Yeah, it will diverge. Although the limit as n approaches infinity has that (n+2)/(3n-1) approaches 1/3, the (-1)^n multiplier will have your limit oscillate...it won't be able to converge.

Answer 3

so because (-1)^n diverges, by the theorem if one diverges all will diverge and therefore the sequence will diverge?

Answer 4

Kind of...in order for a sequence to converge, it must head toward a single value - that's the motivation for the definition. As you have that (-1)^n thing attached, you won't have the case where you approach one value...you essentially approach two values: -1/3 and +1/3.

Answer 5

I've got it! Thank you.

Answer 6

No worries :)