Arjang
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 Mar25 revised $\int \sin(ax) \,\mathrm d x$ edited title Mar25 comment Why does tan(t) touch the unit circle at (1,0)? angle in radians or degrees? Mar25 revised $\left(\frac{a^2+d^2}{a+d}\right)^3+\left(\frac{b^2+c^2}{b+c}\right)^3\geq\left(\frac{a+b}{2}\right)^3+\left(\frac{c+d}{2}\right)^3$ edited title Mar25 revised $\frac{a^2+b^2+c^2}{a^5+b^5+c^5}+\cdots+\frac{d^2+a^2+b^2}{d ^5+a^5+b^5}\le\frac{a+b+c+d}{abcd}$ edited title Mar25 revised $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\geq \frac{3}{\sqrt{2}}$ edited title Mar25 revised $\sum_{i=1}^{n} (3i + 2n)$ edited title Mar25 revised $\lim _{n \rightarrow \infty }a_{n}=\sqrt{a_{n-2}a_{n-1}}$ , $a_1=1, a_2=2$ edited title Mar25 revised $\iiint_WfdV=\int_{A}^{B}\int_{C}^{D}\int_{E}^{F} d\rho d\varphi d\theta$ edited title Mar25 revised $\lim _{x\rightarrow\infty} \left(\sqrt{(1+ab)(1+ab+(1-a)cx^{-d})}-\sqrt{ab(ab+(1-a)cx^{-d})}\right)^{-x}$ edited title Mar25 revised $\lim_{n\rightarrow \infty} (n+1)\cdot x^{n\cdot n!} < 1$ edited title Mar25 revised Is taking limits an operator? added 1 characters in body Mar25 answered Is taking limits an operator? Mar24 comment Show that if $1+\frac {1}{2}+\frac{1}{3}+\cdots +\frac {1}{p-1}=\frac {a}{b}$then a is divisible by $p^2$ @AnindyaGhatak : never mind, thanks to this duplicate question now I know about wolstenholme's theorem. This question should be left as an alternative pointer to proof of wolstenholme's theorem. +1 from me. Mar24 revised Show that if $1+\frac {1}{2}+\frac{1}{3}+\cdots +\frac {1}{p-1}=\frac {a}{b}$then a is divisible by $p^2$ added 161 characters in body; edited title Mar24 comment Show that if $1+\frac {1}{2}+\frac{1}{3}+\cdots +\frac {1}{p-1}=\frac {a}{b}$then a is divisible by $p^2$ @Abhijit : I am assuming he means divisible, I am editing the title accordingly Mar24 revised If $U_0 = 0$ and $U_n=\sqrt{U_{n-1}+(1/2)^{n-1}}$, then $U_n < U_{n-1}+(1/2)^n$ for $n > 2$ edited title Mar24 revised $\iiint e^{-x^2-2y^2-3z^2}dV$ edited title Mar24 revised $( \forall k \in \mathbb N ,\, n \neq k^2 \implies \sqrt{n} \not \in \mathbb Q)\implies \sqrt{2}+ \sqrt{3} \not \in \mathbb Q$ edited title Mar24 comment Infinite Sequence of Inscribed Pentagrams - Where does it converge? @JulienClancy : thanks, I wasn't sure with my drawings either, but I am still looking for some relationship between consecutive inscribes. Mar24 comment Infinite Sequence of Inscribed Pentagrams - Where does it converge? Is every second inscription similar? by that I mean if $p_0$ is the original pentagram, and $p_1,p_2,\cdots$ are the follow up inscriptions then all $p_0,p_2,p_4$ and $p_1,p_3,p_5$ are just scaled down versions of their $p_{k-2}$th ancestor pentagram?