query: Question about a nested radical identity of Ramanujan involving $\sqrt 5$
positive_passages.docid: 21826
positive_passages.text: How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
negative_passages.docid: 43453
negative_passages.text: Is ${\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^\sqrt2}}}}^{...}=4$ correct?
negative_passages.docid: 149294
negative_passages.text: How do i prove how $S_5$ is generated by a two cycle and a five cycle?
negative_passages.docid: 81058
negative_passages.text: Evaluate $6^{433} \pmod {21}$ and a proving question
negative_passages.docid: 36388
negative_passages.text: How to derive this Combinatorial identity
negative_passages.docid: 43300
negative_passages.text: The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
negative_passages.docid: 39642
negative_passages.text: Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
negative_passages.docid: 143409
negative_passages.text: Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
negative_passages.docid: 8589
negative_passages.text: $\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
negative_passages.docid: 60475
negative_passages.text: Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$
negative_passages.docid: 19174
negative_passages.text: Definition of convergence of a nested radical $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$?
negative_passages.docid: 141371
negative_passages.text: Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$
negative_passages.docid: 105238
negative_passages.text: Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$
negative_passages.docid: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 102398
negative_passages.text: Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 144765
negative_passages.text: Solving $\sqrt{x+5} = x - 1$