Question

How do you determine whether the sequence `a_n=(n^3-2)/(n^2+5)` converges, if so how do you find the limit?

Answer 1

No.

Explanation:

If the sequence is convergent then its limit to infinity would be a finite number.

`(n^3-2)/(n^2+5)`

We can disregard the constants, since this is a limit to infinity.So:

`n^3/n^2=n/1`

`lim_(n->oo)(n/1)= oo`

This doesn't limit to a finite value, therefore it is non-convergent.