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Numerade Educator

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Problem 25 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = \frac {n^4}{n^3 - 2n} $

Answer

1 Diverges

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Video Transcript

to figure out whether or not the sequence converges or diverges. I need to look at the limit as n goes to infinity of AM and figure out if that's the women exists. And if it's a finite number so we can do the trick where we look at the biggest power of in and the denominator and divide the top in the bottom, I at number so we can divide the top on the bottom by in cubed, and we have been on top than one minus two over and squared in the denominator. And as long as you don't get something an indeterminate form, you're allowed toe put the limit on top and the limit on the bottom. So as long as you don't get something like infinity over infinity or something divided by zero, then your levity. This here. We're just going to get infinity over one, so that's fine. That's not indeterminant form. It's just infinity. The limit does exist, but infinity is not a real number, so the limit didn't go to anything finite. So we say that the sequence diverges