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JH
Numerade Educator

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Problem 14 Easy Difficulty

Determine whether the series converges or diverges.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {1}{\sqrt [3]{3n^4 + 1}} $

Answer

Convergent.

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Video Transcript

less determined whether the Siri's convergence or diverges now, since three into the fourth plus one, is bigger than three into the fourth. This means at the Q brew is also larger. But this means that if I flip both sides and after flipped inequality as well, therefore over here, I could actually just use less than I guess, because I am going to infinity. I should put equals just in case they're they're both infinity, So one over Q Brew of three. Answer the fourth. Now let's go in and simplify this. So that's our P value. We see that we have a P series here and equals one to Infinity won over the humor of three times and so the for over three. So this convergence by the Peters with P equals for over three, and that's bigger than one. So by the comparison test, our Siri's also emerges, and that's your final answer.