Michael Lugo
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 Nov 2 answered Probability of G Good elements and B Bad elements. Nov 2 comment Probability of G Good elements and B Bad elements. (c) is correct, but is there an easy way to see that those four expectations are the same? Nov 1 comment Trouble with integrating $\frac{\arctan (x)}{x}$ If $\lim_{x \to \infty} f(x) = 0$, then $\lim_{x \to \infty} \int_0^x f(t) \: dt$ can be finite or infinite. Consider the cases $f(t) = 1/(1+t^2)$ (finite integral) and $f(t) = 1/(1+t)$ (infinite integral). Which of these cases does $f(t) = \arctan(t)/t$ resemble more closely? Nov 1 comment Weak Lower Bound in Apostol's “Number Theory”? It may be possible that when the book was originally written, the greatest known Fermat composite was smaller, and in later editions/printings the number was changed but not the accompanying comment. (I don't know the publication history of this book.) Nov 1 awarded Guru Oct 31 comment Finding the maximum number with a certain Euler's totient value The sequence you're looking for is at oeis.org/A006511 -- although there are no references there. There's some Mathematica code but it looks like it relies on Mathematica's "phiinv" function. You might want to try looking for references to the "inverse totient" function. Oct 31 answered Proof for convergence of a given progression $a_n := n^n / n!$ Oct 30 comment Is $x^3-yx^2 = y^3-xy^2$ transitive? With a bit of rewriting you can show that $xRy$ if and only if $(x-y)^2 (x+y) = 0$. This should help. Oct 29 comment Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$ What's the derivative of the numerator as $n \to \infty$? To find that you'd need to find a way to interpret the numerator when $n$ is not an integer. Oct 29 answered Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$ Oct 28 answered Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? Oct 28 comment Multiple-choice question about the probability of a random answer to itself being correct More discussion of this at metafilter: metafilter.com/108902/Try-not-to-think-too-hard Oct 28 comment With Euler's method for differential equations, is it possible to take the limit as $h \to 0$ and get an exact approximation? In theory, yes. In practice, rounding error accumulates and this doesn't work. Oct 28 answered Finding a harmonic number closest to a given large integer Oct 24 answered Can I use my powers for good? Oct 18 comment The Power of Taylor Series Of course, some smart-ass will ask "how do you compute $\sqrt{3}$"? (This isn't hard - Newton's method converges quickly, for example, or one could find the series for $\sqrt{x}$ around $x=4$ - but it's worth thinking about beforehand.) Oct 17 comment What's the General Expression For Probability of a Failed Gift Exchange Draw I think you mean $\left({n-1 \over n}\right)^{2n} \to (1/e)^2$, which seems to agree better with numerical results. Oct 16 comment Distribution of a maximum @MichaelHardy I've been guilty of using "randomly" to mean "uniformly distributed", although generally only for uniform distributions over a finite set. Oct 13 comment Probability Game: Find probability she wins the game on nth point played for n=4,5,6 That is also my interpretation. Oct 7 answered Am I over thinking this 5th grade coin flipping homework problem?