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anonymous
 4 years ago
evaluate limit of n>infinity of (1)/[(n4)/(n)]^n
anonymous
 4 years ago
evaluate limit of n>infinity of (1)/[(n4)/(n)]^n

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nikvist
 4 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{n\rightarrow\infty}\frac{1}{\left(\frac{n4}{n}\right)^n}=\lim_{n\rightarrow\infty}\left(\frac{n}{n4}\right)^n=\lim_{n\rightarrow\infty}\left(1+\frac{4}{n4}\right)^n=\]\[=\lim_{n\rightarrow\infty}\left[\left(1+\frac{4}{n4}\right)^\frac{n4}{4}\right]^\frac{4n}{n4}=\exp{\left(\lim_{n\rightarrow\infty}\frac{4n}{n4}\right)}=e^4\]
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