more sequences

[jellybean]

does the sequence converge or diverge?

an = (-1)^n*(n^3)/n^3 +2n^2+1

so i divided top and bottom by n^3 to get (-1)^n/(2/n) + (1/n^3))
I dont know if this is right and i dont know what to do after if it is right.

 

[Gene]

a_n = (-1)^n*(n^3)/n^3 +2n^2+1
doesn't make sense. it =
(-1)^n + 2n^2+1
so I assume you mean
a_n = (-1)^n*(n^3)/(n^3 +2n^2+1)

so i divided top and bottom by n^3 to get (-1)^n/(1 + 2/n + 1/n^3)
which approaches
...+1,-1,+1,-1,+1...

BTW I used a_n to get a_n