query: Find the limit of $a_{n+1}=\cos(a_n)$
positive_passages.docid: 133279
positive_passages.text: Does $\lim_{n\to\infty}\underset{n}{\underbrace{\cos(\cos(...\cos x))}}$ exist?
negative_passages.docid: 127001
negative_passages.text: Evaluate $\lim_{x\to \infty} \cos (\sqrt {x+1})-\cos (\sqrt x)$
negative_passages.docid: 28669
negative_passages.text: Find limit of the following sequence: $\frac{\log(n+1)}{\log(n)}$?
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: 20773
negative_passages.text: Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
negative_passages.docid: 19100
negative_passages.text: Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$
negative_passages.docid: 39752
negative_passages.text: Is there a limit of $\cos(n!)$?
negative_passages.docid: 37158
negative_passages.text: upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$
negative_passages.docid: 123253
negative_passages.text: Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
negative_passages.docid: 37394
negative_passages.text: How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
negative_passages.docid: 50673
negative_passages.text: Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
negative_passages.docid: 97047
negative_passages.text: Limit for sequence $a_{m+n}\leq a_m+a_n$
negative_passages.docid: 15982
negative_passages.text: Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$
negative_passages.docid: 29266
negative_passages.text: Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
negative_passages.docid: 146529
negative_passages.text: Finding the limit $ \lim_{x\to a^+} \frac{\cos(x)\ln(x-a)}{\ln(e^x-e^a)} $
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 145913
negative_passages.text: Find $\lim_{x\rightarrow 0} \frac{\cos x - 1}{x}$