query: Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+\dots}} }$
positive_passages.docid: 27068
positive_passages.text: Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
negative_passages.docid: 11707
negative_passages.text: If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
negative_passages.docid: 107200
negative_passages.text: Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$
negative_passages.docid: 38975
negative_passages.text: Find the value of $\textrm{cosec}^2\left(\frac\pi7\right) +\textrm{cosec}^2\left(\frac{2\pi}7\right)+\textrm{cosec}^2\left(\frac{4\pi}7\right)$
negative_passages.docid: 20055
negative_passages.text: Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
negative_passages.docid: 40973
negative_passages.text: How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?
negative_passages.docid: 76560
negative_passages.text: How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?
negative_passages.docid: 25193
negative_passages.text: Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$
negative_passages.docid: 14386
negative_passages.text: Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
negative_passages.docid: 115825
negative_passages.text: Unnesting $\sqrt{1+\sqrt2}$
negative_passages.docid: 130565
negative_passages.text: Find all solutions to $x^3+(x+1)^3+ \dots + (x+15)^3=y^3$
negative_passages.docid: 49028
negative_passages.text: Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$
negative_passages.docid: 26876
negative_passages.text: How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?
negative_passages.docid: 13085
negative_passages.text: Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
negative_passages.docid: 137027
negative_passages.text: Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
negative_passages.docid: 96875
negative_passages.text: Finding the value of $x^{x^2}+x^{x^6}$ given that $x^{x^4}=4$