Determine if the sequence converges or diverges.

an=(n^4)/(n^3-8n)

1 answer

We can rewrite the sequence as

an = n(n^3)/(n^3 - 8n)

Dividing both the numerator and denominator by n^3, we get

an = n/(1 - 8/n^2)

As n gets large, the denominator approaches 1, and the entire fraction approaches infinity. Therefore, the sequence diverges to infinity.