query: Which exponents r>0 is the limit finite
positive_passages.docid: 147887
positive_passages.text: When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
negative_passages.docid: 39752
negative_passages.text: Is there a limit of $\cos(n!)$?
negative_passages.docid: 101904
negative_passages.text: Why does this limit exist $x^{x}$
negative_passages.docid: 56048
negative_passages.text: Limit at infinity of $x^{1/x}$
negative_passages.docid: 97369
negative_passages.text: Does the limit of $e^{-1/z^4}$ as $z\to 0$ exist?
negative_passages.docid: 12914
negative_passages.text: What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
negative_passages.docid: 56728
negative_passages.text: Question about limit points of a Subset of $\mathbb{R}$
negative_passages.docid: 8503
negative_passages.text: Limit of $L^p$ norm when $p\to0$
negative_passages.docid: 54952
negative_passages.text: Is it true that $\limsup\sqrt[n]{|a_n|}=\limsup\sqrt[n]{|a_n-a_{n-1}|}$, ($n>1$), where $\{a_n\}$ does not have a finite limit?
negative_passages.docid: 78941
negative_passages.text: proof that an alternative definition of limit is equivalent to the usual one
negative_passages.docid: 67420
negative_passages.text: Limit of quotient sequence
negative_passages.docid: 6821
negative_passages.text: Proof that Limit of the Log is the Log of the Limit
negative_passages.docid: 65137
negative_passages.text: Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
negative_passages.docid: 72960
negative_passages.text: How to prove this limit composition theorem?
negative_passages.docid: 104878
negative_passages.text: What is the limit $\lim\limits_{n \to \infty} \frac{n^{\sqrt{n}}}{2^n}$?
negative_passages.docid: 103055
negative_passages.text: Proving the quotient rule for limits
negative_passages.docid: 32742
negative_passages.text: The limit of $\frac{|A_n|}{n^2}$