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

Oct 16, 2017

No.

#### Explanation:

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

$\frac{{n}^{3} - 2}{{n}^{2} + 5}$

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

${n}^{3} / {n}^{2} = \frac{n}{1}$

${\lim}_{n \to \infty} \left(\frac{n}{1}\right) = \infty$

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