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New posts in radicals
Proving $\left(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}}\right)\left(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x+\cdots}}}}\right)=x$
calculus
sequences-and-series
limits
radicals
nested-radicals
Using the fact that $\sqrt{n}$ is an irrational number whenever $n$ is not a perfect square, show $\sqrt{3} + \sqrt{7} + \sqrt{21}$ is irrational.
radicals
irrational-numbers
Comparing the magnitudes of expressions of surds
arithmetic
radicals
Find the real roots for $\displaystyle \sqrt[4]{386-x}+\sqrt[4]{x}=6.$
algebra-precalculus
polynomials
contest-math
systems-of-equations
radicals
Find the limit of $\frac{(n+1)^\sqrt{n+1}}{n^\sqrt{n}}$.
sequences-and-series
limits
exponentiation
radicals
Continuity of composition of root and floor function
continuity
radicals
epsilon-delta
ceiling-and-floor-functions
Find the limit $\lim_{n\to\infty}\left(\sqrt{n^2+n+1}-\left\lfloor\sqrt{n^2+n+1}\right\rfloor\right)$ [duplicate]
sequences-and-series
limits
radicals
integers
ceiling-and-floor-functions
How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity? [duplicate]
real-analysis
limits
factorial
radicals
How do I prove that $\sqrt{20+\sqrt{20+\sqrt{20}}}-\sqrt{20-\sqrt{20-\sqrt{20}}} \approx 1$
numerical-methods
approximation
radicals
nested-radicals
Unexpected result from Euler's formula
complex-numbers
radicals
fake-proofs
Contradiction with Power functions with odd exponent? [duplicate]
algebra-precalculus
complex-numbers
exponentiation
radicals
fake-proofs
Which is larger $\sqrt[99]{99!}$ or $\sqrt[100]{100!}$
problem-solving
radicals
How to solve $ \sqrt{x^2 +\sqrt{4x^2 +\sqrt{16x^2+ \sqrt{64x^2+\dotsb} } } } =5\,$?
sequences-and-series
recurrence-relations
radicals
nested-radicals
Simplify: $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\ldots+\sqrt{10+\sqrt{99}}}{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\ldots+\sqrt{10-\sqrt{99}}}$ [duplicate]
summation
radicals
Novel (?) proof of the irrationality of $\sqrt3$ [duplicate]
radicals
rationality-testing
Is the value of $\sin(\frac{\pi}{n})$ expressible by radicals?
trigonometry
natural-numbers
radicals
A little more on $\sqrt[3]{\cos\bigl(\tfrac{2\pi}7\bigr)}+\sqrt[3]{\cos\bigl(\tfrac{4\pi}7\bigr)}+\sqrt[3]{\cos\bigl(\tfrac{8\pi}7\bigr)}$
trigonometry
prime-numbers
radicals
roots-of-unity
On $_2F_1(\tfrac13,\tfrac23;\tfrac56;\tfrac{27}{32}) = \tfrac85$ and $_2F_1(\tfrac14,\tfrac34;\tfrac78;\tfrac{48}{49}) = \tfrac{\sqrt7}3(1+\sqrt2)$
calculus
radicals
hypergeometric-function
experimental-mathematics
Cube root of two $\sqrt[3]2$ continued fraction
radicals
continued-fractions
What is the closed-form for $\displaystyle\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + mn+41n^2}$?
sequences-and-series
algebraic-number-theory
radicals
zeta-functions
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