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Numerade Educator

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Problem 24 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = \frac {3 + 5n^2}{1 + n} $

Answer

The sequence diverges

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Video Transcript

to figure out whether or not we get convergence. We need to look at this limit. Mhm. Mhm. Now we can use the trick where we divide the top and the bottom by the largest power of n appearing in the denominator sort by the top and the bottom by and okay, And then put the limit on top. Put the limit on the bottom. And this is something that we're allowed to do as long as we don't get something indeterminate form. So as long as you don't have infinity over infinity or dividing by zero or anything but here we won't be in that setup. We'll have infinity over one, which is fine. That will give us infinity. So that means that we diverge because infinity is not a real number. So to converge, this limit would need to exist, and it would need to be equal to some finite number