# Jean-Sébastien

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 Feb26 comment Finding out the coeffcient next to $x^2$ in $(\cdots(x-2)^2-2)^2\cdots-2)^2$. I don't know why it is, but it seems the recurrence is $a(n)=20a(n-1)-64a(n-2)$, which gives the solution $(4*16^n-4^n)/3.$ Feb19 comment Prove that $\sum_i\sum_j a_{ij}=\sum_j\sum_i a_{ij}$ Jan9 reviewed Approve suggested edit on proving a specific trig inequality 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 suggested edit on 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 suggested edit on $x^{y^z}$: 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