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Numerade Educator



Problem 19 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {n^3}{n^4 + 4} $




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Video Transcript

this problem. We want to determine if the Siri's converges or diverges, so we'll use an integral again. We're just gonna have to change what's inside of it. It will be from one to infinity, though, because the summation is from one to infinity. In this case, what we're gonna have is X cube over X to the fourth class four. What we see is this is undefined. So it's ultimately going to mean that the Siri's diverges on beacon figure out why this is the case. Because, um, what we see is, if we evaluate this inter rule, what will end up getting in the natural log? Because we have this done here, the fractional value. So when we get these natural logs on DWI evaluate, it will end up getting, um, an infinite value. So with that, we see that the integral evaluated at this is infinity. Andi, therefore, we know that the integral diverges, um, and since the integral diverges, that tells us that the Serie ultimately diverges