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Numerade Educator

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Problem 34 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = e^{2n/(n + 2)} $

Answer

converges to $e^{2}$

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Video Transcript

we need to look at limit as n goes to infinity, have a N. If that's that limit exists and is finite than our sequence converges. Otherwise our sequence diverges. The exponential function is a continuous function, which means that we're allowed to pull the limit up top into the exponents can. Now we divide the top and the bottom by end to get to divided by one class two over end, as in goes to infinity. This two over and is going to go to zero. And we're just going to get eat to the two over one, which is the same thing as you do too. So we do converge. We converged, Tio, he squared.