Michael Lugo
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 Jun 10 reviewed Close Limit of an increasing function Jun 10 reviewed Leave Open Equilibrium in difference equations Jun 9 answered Solving recurrence similar to Catalan number recurrence Jun 5 comment Is there a closed form for $\sum_{n=0}^{+\infty} \frac{1}{\sqrt {n!}}$? It seems quite unlikely. See mathforum.org/kb/message.jspa?messageID=5628902 or wilmott.com/messageview.cfm?catid=34&threadid=44616 (which can be found by computing the sum numerically and googling the resulting value). Jun 3 answered Name of the highest power of 2 smaller than or equal to a given number May 14 comment Prove that using generating function:For any $n ,k\in N$, the number of partitions of $n$ into parts If you're being asked this, I suspect you've seen the generating-function proof for the case $k = 1$ - that is, that the number of partitions into parts which appear at most 1 time ("partitions into distinct parts") is the same as the number of partitions into parts not divisible by 2 ("partitions into odd parts"). Can you generalize this proof? May 11 comment Find a linear reccurrence relation where a(n) is the number of subsets of {1,2,3,…,n} not containing three consecutive numbers. This is a duplicate of math.stackexchange.com/questions/86249/… , although that question wasn't answered so I recommend leaving this one open. May 7 answered Let $a,b$ be relative integers such that $2a+3b$ is divisible by $11$. Prove that $a^2-5b^2$ is also divisible by $11$. May 4 reviewed Close Famous Problems the Experts Could not Solve May 4 reviewed Leave Open What is meant by a “$S$-strictly diagonally dominant matrix” in the book 'Geršgorin and His Circles' May 4 reviewed Close A nice set of squares. Apr 30 reviewed Close What are numbers? Apr 30 reviewed Close Proof verification for proving $\forall n \ge 2, 1 + \frac1{2^2} + \frac1{3^2} + \cdots + \frac1{n^2} < 2 − \frac1n$ by induction Apr 30 reviewed Leave Open Help with finding range and equation of a position vector (projectile) Apr 29 reviewed Leave Open how to combine angle rotations along different axes into one rotation along a single vector Apr 29 reviewed Leave Open Statistics Problems, I don't understand what this means.. Apr 29 answered Collection all cards in a cardgame Apr 29 comment If $n$ is composite, then $((n-1)!)^2 \equiv 0 \pmod n$ 4 is the only counterexample: see e. g. Benoit Cloitre's comment at oeis.org/A046022 Apr 29 reviewed Looks OK Evaluate $\lim _{n\to \infty }\int_1^2\:\frac{x^n}{x^n+1}dx$ Apr 29 reviewed Looks OK Show that there exists an idempotent element such that $Ra=Re$ holds for ring $R$