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Prove that the given sequence ${a_n}$ diverges to infinity.

$a_n=\frac{n^3+5}{-n^2+8n}$

I believe that the sequence diverges to -infinity. And I have this for my proof so far:

Let $M>0$ and let $N=$ ?. Then $n>N$ implies... I am confused on how to solve for the N. I believe I have to make the numerator larger and denominator smaller, but I have a hard time visualizing this.

2 Answers 2