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Numerade Educator

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Problem 23 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = \frac {3 + 5n^2}{n + n^2} $

Answer

5 as $n \rightarrow \infty$. Converges

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Video Transcript

to figure out whether or not this converges. We just need to figure out whether or not this limit exists. Okay, so we could do the trick where we divide the top and the bottom by the largest power of end that we see in the denominator. It's in this case we'd be dividing the top in the bottom. Bye. In squared, as in Goes to infinity three over and squared, goes to zero and one over and goes to zero as well. So we just have five over one, which is five. So it does converge and it converges two five.