query: Lower limit of $\sqrt[n]{1^n+2^n+...+n^n}$ with sandwich rule
positive_passages.docid: 7
positive_passages.text: Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
negative_passages.docid: 98306
negative_passages.text: Limit of $n/\ln(n)$ without L'Hôpital's rule
negative_passages.docid: 106527
negative_passages.text: Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
negative_passages.docid: 113891
negative_passages.text: The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
negative_passages.docid: 18079
negative_passages.text: Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
negative_passages.docid: 135159
negative_passages.text: Limits using L'Hopital's rule $\lim_{x\to0^+} (x^{x^x-1})$
negative_passages.docid: 41203
negative_passages.text: Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$
negative_passages.docid: 30167
negative_passages.text: Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
negative_passages.docid: 32742
negative_passages.text: The limit of $\frac{|A_n|}{n^2}$
negative_passages.docid: 60036
negative_passages.text: How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
negative_passages.docid: 61698
negative_passages.text: Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$
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: 4024
negative_passages.text: Finding the limit of $\frac {n}{\sqrt[n]{n!}}$
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
negative_passages.docid: 56056
negative_passages.text: Find $\lim_{n\to\infty}2^n\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt2}}}}_{n \textrm{ square roots}}$.
negative_passages.docid: 125860
negative_passages.text: Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$