help with the following sequence

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help with the following sequence

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[a _{n}=e ^{2n/(n+2)} \]
I ln both side ( after putting the limit) and then used the hospital rule but my book solved it in a completely different way :/ and came to a different answer. So, I'm kinda lost on how to solve it
multiplied ln to both side*

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what does "solve" mean in this context?
you have \[a_n=e^{\frac{2n}{n+2}}\] what are you trying to find?
if you are looking for \[\lim_{n\to \infty}e^{\frac{2n}{n+2}}\] then since \[\lim_{n\to \infty}\frac{2n}{n+2}=2\] the answer is \(e^2\)
Sorry I was gone for a while but yea it was what I was looking for^^

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