Finding Convergence, Limits and values

[smutangama]

Don't really know how to get round this, the -1^n confuses me.

Homework Statement

Determine whether the following sequence {a_n} converges as n→∞?
if it does, find lim_n→∞a_n

Homework Equations

a_n=(3n+(-1)ⁿ )/ (n³+2)

Homework Statement

 

[HallsofIvy]

What is your purpose in posting this? It does not appear to be to get an answer or for help because you have made no to do it yourself- so you are clearly not very interested in the answer!

An obvious first step, since it asks for "the limit as n goes to infinity" would be to see what you get if you replace n with some really large number- say 10000000. Have you tried that?

 

[smutangama]

I'm sorry, I'll post better next time. I'm new to the site and still trying to get used to things. I am not really good at limits. It confuses me.
I needed help with the question, I came up with zero at the end but I wasn't sure if I was right.
Also does this mean it diverges?

 

[micromass]

Can you explain how you found $0$?

 

[smutangama]

I used a method where I divided the numerator and denominator by the highest power which was n^3. From there I was left with 0/1 which is zero. Was that right?

 

[HallsofIvy]

I'm sorry, I'll post better next time. I'm new to the site and still trying to get used to things. I am not really good at limits. It confuses me.
I needed help with the question, I came up with zero at the end but I wasn't sure if I was right.
Also does this mean it diverges?

What is your understanding of the words "converge" and "diverge"? You seem to be saying that "because the limit is 0, it diverges". Is that what you are saying?

 

[smutangama]

my understanding is if it converges, the total sum is the limit of the sequence or something along those lines. Maybe I just have the entire concept wrong, that's why I'm finding it confusing. Can you please help me with a simple explanation of the two?