# Jean-Sébastien

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 Apr12 comment No. of 4 digit nos. which can be formed containing at most 2 digits? This "question" is related to an attempted answer by OP here math.stackexchange.com/questions/154713/… Apr10 comment Help with this combinatorial proof $\sum\limits_{k=1}^nk^2(k-1){n\choose k}^2 = n^2(n-1){2n-3\choose n-2}$ considering $n\ge2$ Where did you get this formula? left-hand side gives $480$ and right hand side gives $160$ for $n=4$... Apr10 comment What does this equal? $6\div 2(1+2)$ how does someone get $7$? Apr10 comment Are the two integrals equivalent? Yes they are indeed the same Apr5 comment Simple way to see this integral is 0? Mar31 comment $f(x)=x$ if $x$ is rational , $f(x)=1-x$ if $x$ is irrational, at what point this function is continuous? You beat me to it, +1 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 $\sum_i\sum_j a_{ij}=\sum_j\sum_i a_{ij}$ Oct23 comment Integral of product of two measurable functions This is essentially a special case of Holder's inequality. Oct22 comment Mean value of the image of an exponentiallly distributed time under a smooth curve $f(t)$ should be $\phi(t)$ in 3. 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 $1,2\mod 4$ 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 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$even then Oct16 comment Why do we call it a$\sigma$-algebra? In French, we even use the word "Tribu", which makes even less sense Oct16 comment Is there a fast way to compute coefficient of some term of the product of some series'? @user100508 Yes there is someting to do in that case, perhaps ask a new question for that particular case. Oct15 comment Is there a fast way to compute coefficient of some term of the product of some series'? @user100508 Using$A*B$to be the cauchy product of two series, you could derive that it is in fact a convolution. In particular, it is associative, so for$A*B*C$, start by computing$D=A*B$and then$D*C\$. I do not know of a more elegant formula other than the one you'd get arranging all the sums this process give you