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 May30 comment Finding an expression to represent this pattern You really need to tell us more about the source of these numbers. In particular, are the decimal numbers rounded or exact? May30 comment For all integrable $f:[-1,1]\mapsto \mathbb{R}$ prove that $\int_{-1}^1f^2(x)\ge\frac12(\int_{-1}^1f(x))^2+\frac32(\int_{-1}^1xf(x))^2$ Please spell Cauchy-Schwarz correctly. May30 comment little inequality conjecture Please spell Cauchy-Schwarz correctly. May29 comment Is the area of a pentagon inscribed into an ellipse independent of starting point? @DavidSpeyer It doesn't matter where the origin is, one can just add the five expressions. May28 comment Is the area of a pentagon inscribed into an ellipse independent of starting point? Your link states: In the comments below, it is stated that this conjecture is not true. However, the comments are behind a login wall. Could you please tell us what the comments say? May25 comment Number of non-decreasing sequences @vonbrand But once is less than twice, so it is not most frequent. May25 comment Number of non-decreasing sequences Do you have a conjecture? May13 comment Prove the sequences $\lfloor \alpha n\rfloor$ and $\lfloor \beta n\rfloor$ are disjoint @GabrielR. How many of the numbers in the first sequence are smaller than $n$? May13 comment Prove the sequences $\lfloor \alpha n\rfloor$ and $\lfloor \beta n\rfloor$ are disjoint @i707107 Do you think that this is a good hint? May13 comment Existence of functions which satisfy some conditions For you, too: spikedmath.com/170.html May13 comment Existence of functions which satisfy some conditions spikedmath.com/170.html May13 comment Prove the sequences $\lfloor \alpha n\rfloor$ and $\lfloor \beta n\rfloor$ are disjoint Try to count how many numbers in both sequences together are of size at most $n$. May12 comment How do we pronounce this symbol? @Mathias711 It used to be one of the community ads, I do not know if it is now. May12 comment How do we pronounce this symbol? Detexify can sometimes help with this kind of question: detexify.kirelabs.org/classify.html May11 comment Inverse Identity + Constant Matrix However, I would be quite impressed if someone found this without ever having seen something similar. May11 comment Inverse Identity + Constant Matrix @AimForClarity First of all, I have seen the matrix with only 1s in other problems before, so its properties are already at the back of my head. In general, you can express any inverse matrix as polynomial in the matrix (just multiply the minimal polynomial by the inverse), so I am already motivated to look at this. To find the minimal polynomial directly, it is clearly useful to calculate $B^2$ and the identity $B^2=nB$ tells me that the minimal polynomial for $I+B$ must have degree 2, so the expression for the inverse (if it exists) must have degree 1 in $B$. May11 comment Generalization of Binomial Coefficients Congruence @sm654567 I am not sure what you mean. What you want is usually the key lemma in any proof of Lucas theorem and it only uses elementary facts, the binomial theorem and the fact that $p$ does not divide factorials of smaller numbers. May7 comment Inverse Identity + Constant Matrix That is correct (if you replace a with c). May4 comment What's the behavior of $\displaystyle\sum_{n=1}^\infty (z+\sqrt{5}+2i)^{n!}$ outside its radius of convergence? @oxbadfood You have edited your mistake AFTER my comment, so it is not good form to ask "why are you telling it me now" as if the timeline were the reverse. Also, your new title (about behaviour outside the radius) is in direct contradiction to your actual question (behaviour ON the circle of convergence) which I already answered. I am giving up on this question. May4 comment What's the behavior of $\displaystyle\sum_{n=1}^\infty (z+\sqrt{5}+2i)^{n!}$ outside its radius of convergence? @BobbyOcean I am not opposed to using the limsup formula, I am opposed to your wrong claim that "the ratio test yields no information". It is perfectly reasonable to use it for this problem.