Sunday, March 4, 2018

calculus - Limit $ lim_{n rightarrow infty}sqrt{(1+frac{1}{n}+frac{1}{n^3})^{5n+1}} $


What's the limit of this?
$$
\lim_{n \rightarrow \infty}\sqrt{\left(1+\frac{1}{n}+\frac{1}{n^3}\right)^{5n+1}}
$$




Can't find a way to solve it, I tried to use something looks like $(1+1/n)^n$ but didn't succeed.




Many thanks!

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