By using the fact that $\log(n)<<n$，evaluate $\lim n^{1/n}$.
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
120336
Evaluation of $\lim_{n\rightarrow \infty}\binom{2n}{n}^{\frac{1}{n}}$
72282
Let$\ p_n$ be the$\ n$-th prime. Is$\ \lim_{n\to\infty} \log \log n \prod_{i=1}^{\lfloor \log n \rfloor} \frac{p_i-1}{p_i}>0$?
56902
Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$
31889
The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
65137
Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
81997
Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$
6304
Evaluate $\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $
68368
Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$
53688
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
27511
Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
33610
Evaluate $\displaystyle \lim_{n\to \infty}\sqrt[n]{n!}$
115111
Limit of the sequence $nx_{n}$ where $x_{n+1} = \log (1 +x_{n})$
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
114412
Limit $\lim_{n\to \infty} \frac{1}{2n} \log{2n\choose n}$
61846
Evaluation of $\lim_{n\rightarrow \infty}\frac{1}{2n}\cdot \ln \binom{2n}{n}$
1930
Limit of $\frac{\log(n!)}{n\log(n)}$ as $n\to\infty$.