query: prove the limit of $k^{1/k}$ is $1$
positive_passages.docid: 30160
positive_passages.text: How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
negative_passages.docid: 149792
negative_passages.text: Show that $\lim_{p \to 0} \mathbb {E} [(X^p-1)/p ] = \mathbb{E} [\log X]$
negative_passages.docid: 72693
negative_passages.text: Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
negative_passages.docid: 70491
negative_passages.text: If $\sum_{n=1}^\infty a_n$ converges, prove that $\lim_{n\to \infty} (1/n) \sum_{k=1}^n ka_k = 0$.
negative_passages.docid: 25206
negative_passages.text: How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
negative_passages.docid: 108971
negative_passages.text: Finding the limit of $\sqrt[n]{{kn \choose n}}$
negative_passages.docid: 31930
negative_passages.text: Given the sequence $(x_n)$ is unbounded, show that there exist a subsequence $(x_{n_k})$ such that $\lim(1/x_n)=0$.
negative_passages.docid: 126374
negative_passages.text: Limit of $2^{1/n}$ as $n\to\infty$ is 1
negative_passages.docid: 144422
negative_passages.text: How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
negative_passages.docid: 109907
negative_passages.text: How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
negative_passages.docid: 66441
negative_passages.text: Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
negative_passages.docid: 110275
negative_passages.text: Let $p>0$. Show the $\lim_{n\to\infty}(a^n/n^p)$ is equal to:
negative_passages.docid: 95962
negative_passages.text: proving a theorem from limit using Hopital rule
negative_passages.docid: 7510
negative_passages.text: Methods to find $\lim\limits_{n\to\infty}\frac1n\sum\limits_{k=1}^nn^{1/k} $
negative_passages.docid: 108929
negative_passages.text: Proving the limit of a function of a sequence is equal to the function of the limit of that sequence
negative_passages.docid: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 43246
negative_passages.text: Showing that if $a<b$, then $a^{1/n} < b^{1/n}$