Jean-Sébastien
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 Jan9 reviewed Approve Prove that $\frac12 < 4\sin^2\left(\frac{\pi}{14}\right) + \frac{1}{4\cos^2\left(\frac{\pi}{7}\right)} < 2 - \sqrt{2}$ Nov29 awarded Civic Duty Oct27 reviewed No Action Needed Find $a\in\mathbb{N}$ such that $n^4+a$ is not prime $\forall n\in\mathbb{N}$ Oct23 revised How to change to same units edited tags Oct23 comment Integral of product of two measurable functions This is essentially a special case of Holder's inequality. Oct23 answered Intuition behind product rule of probability Oct22 answered Proof of Aristarchus' Inequality Oct22 reviewed Approve Polynomial inequality proof Oct22 comment Mean value of the image of an exponentiallly distributed time under a smooth curve $f(t)$ should be $\phi(t)$ in 3. Oct22 reviewed Reviewed prove that quadrangle is isosceles trapezoid Oct21 comment How prove this $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx>0$ I dont have a solution, just some computation with maple/ WA Oct21 comment How prove this $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx>0$ The integral of $\prod_{k=2}^{n}cos(kx)$ seems to be $0$ for values of $n$ congruent to $-1, 0 \mod 4$ and a positive rational fraction of $\pi$ for $1,2\mod 4$ Oct21 reviewed Approve $x^{y^z}$: is it $x^{(y^z)}$ or $(x^y)^z$? Oct20 comment Power series $\sum_{r=1}^{n}x^{r}=\:?$ Almost surely this has been answered here before Oct20 comment $\int_{-\infty}^{\infty} \frac{1}{2\pi} \exp\{ -\frac{1}{2} ((y-x)^2 + x^2) \} dx$ square completion Oct20 answered Are there any open mathematical puzzles? Oct19 answered Determine $a<0$ such that $\int_a^0 f(x) dx = f(a)$ Oct18 comment use combinatorial reasoning to calculate $\sum{\binom{100}{a}\binom{200}{b}\binom{300}{c}}$ To add some reference, this is sometimes known as Vandermonde's convolution Oct17 comment How find the minimum of the value of $n$ such $n^2\equiv 1\pmod{1007}$ Am i missing someting? $1$ will do Oct16 comment Why do we call it a $\sigma$-algebra? @Did doesn't make more sense does it? unles they were auto referencing to the Bourbaki trive they are\$ even then