Question

Product $\left[\sin(x)\cos\left(\frac{x}2\right)\right]^{1/2}\cdot\left[\sin\left(\frac{x}{2}\right) \cos \left(\frac{x}4\right)\right]^{1/4}\ \cdots$

score 182 · Answer 1 · 2020-05-24 07:15:03

182

Views

Product $\left[\sin(x)\cos\left(\frac{x}2\right)\right]^{1/2}\cdot\left[\sin\left(\frac{x}{2}\right) \cos \left(\frac{x}4\right)\right]^{1/4}\ \cdots$

Published on 24 May 2020 - 7:15

score 152 · Answer 2 · 2020-05-26 17:20:38

152

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What is value of $\sqrt[n]{x\sqrt[n]{x\sqrt[n]{x\sqrt[n]{x\ldots}}}}=$?

Published on 26 May 2020 - 17:20

score 608 · Answer 3 · 2026-03-25 11:05:18

608

Views

Find the two complex numbers whose sum is $5 - i$ and product is $8+i$

Published on 25 Mar 2026 - 11:05

score 52 · Answer 4 · 2020-06-02 00:16:49

52

Views

Proving The Nested Radical

Published on 02 Jun 2020 - 0:16

score 242 · Answer 5 · 2020-06-04 07:54:37

242

Views

Find the value of $\sqrt{1+\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\cdots}}}}}$ .

Published on 04 Jun 2020 - 7:54

score 233 · Answer 6 · 2020-06-04 10:33:43

233

Views

Prove that $\frac{1}{\sqrt[3]2}=\sqrt{\frac 5{\sqrt[3]4}-1}-\sqrt{(3-\sqrt[3]2)(\sqrt[3]2-1)}$

Published on 04 Jun 2020 - 10:33

score 99 · Answer 7 · 2020-06-04 11:44:40

99

Views

Calculate $\frac{\pi}{2}-\sin(\frac{\pi}{2})+\sin(\sin(\frac{\pi}{2}))-\sin(\sin(\sin(\frac{\pi}{2})))\cdots$

Published on 04 Jun 2020 - 11:44

score 195 · Answer 8 · 2020-06-11 08:30:21

195

Views

When is $\mathbb{Q}(\sqrt{2+\sqrt{2+\sqrt{2 \ldots}}})$ Galois?

Published on 11 Jun 2020 - 8:30

score 178 · Answer 9 · 2020-06-15 19:37:46

178

Views

Value of $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+...}}}}$.

Published on 15 Jun 2020 - 19:37

score 1.9k · Answer 10 · 2020-06-16 07:46:01

1.9k

Views

Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$

Published on 16 Jun 2020 - 7:46

score 234 · Answer 11 · 2020-06-24 04:45:16

234

Views

An interesting property of nested radicals

Published on 24 Jun 2020 - 4:45

score 592 · Answer 12 · 2020-06-27 13:21:52

592

Views

Can $\cos(2\pi/17)$ be written as nested square roots only?

Published on 27 Jun 2020 - 13:21

score 84 · Answer 13 · 2026-03-25 23:43:28

84

Views

Zero set of nested radicals

Published on 25 Mar 2026 - 23:43

score 128 · Answer 14 · 2026-03-25 21:30:53

128

Views

Example of Devil's nested radicals

Published on 25 Mar 2026 - 21:30

score 111 · Answer 15 · 2020-07-06 01:45:07

111

Views

How do I solve this recursive equation which involves square root?

Published on 06 Jul 2020 - 1:45

List Question

Product $\left[\sin(x)\cos\left(\frac{x}2\right)\right]^{1/2}\cdot\left[\sin\left(\frac{x}{2}\right) \cos \left(\frac{x}4\right)\right]^{1/4}\ \cdots$

What is value of $\sqrt[n]{x\sqrt[n]{x\sqrt[n]{x\sqrt[n]{x\ldots}}}}=$?

Find the two complex numbers whose sum is $5 - i$ and product is $8+i$

Proving The Nested Radical

Find the value of $\sqrt{1+\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\cdots}}}}}$ .

Prove that $\frac{1}{\sqrt[3]2}=\sqrt{\frac 5{\sqrt[3]4}-1}-\sqrt{(3-\sqrt[3]2)(\sqrt[3]2-1)}$

Calculate $\frac{\pi}{2}-\sin(\frac{\pi}{2})+\sin(\sin(\frac{\pi}{2}))-\sin(\sin(\sin(\frac{\pi}{2})))\cdots$

When is $\mathbb{Q}(\sqrt{2+\sqrt{2+\sqrt{2 \ldots}}})$ Galois?

Value of $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+...}}}}$.

Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$

An interesting property of nested radicals

Can $\cos(2\pi/17)$ be written as nested square roots only?

Zero set of nested radicals

Example of Devil's nested radicals

How do I solve this recursive equation which involves square root?

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