Limits of sequences, please help!

Question

lim_n->infinite[ (-1)ⁿ/(n³-12)} 

I dont know what to do with (-1)ⁿ, if it's equal to infinite then if I divide by n³, it's infinite over infinite. I dont understand :S. And the question is if the sequence is divergent or convergent.

Answer 1

-1^infinity = +/- 1 (depending if n is even or odd). (-1 * -1 = +1, -1 * -1 * -1 = -1 etc.)

 

n^3 = infinity

So, you're looking at 1/infinity or 0 as n->infinity.