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seen Oct 3 at 13:23

Sep
30
awarded  Explainer
Sep
29
comment Why are real numbers useful?
Use the binomial distribution.
Sep
25
comment Understanding why Hall's marriage theorem $\Leftrightarrow$ Dilworth's theorem
robertborgersen.info/Presentations/GS-05R-1.pdf gives a number of proofs around all these theorems.
Sep
25
comment Analytic Proof Of ${n\choose r}={n-1\choose r-1}+{n-1\choose r}$
I would call this an 'algebraic' proof. An 'analytic' proof would more likely be a proof using generating functions. Of course everything uses algebra to some extent, but the major category of a proof is the primary strategy.
Sep
25
comment Sum of sequence of cubes and summation on the upper index
$k^3 = 6{k \choose 3} + 3 k^2 -2k $ (I got this by expanding out ${k \choose 3}$). Now eliminate the $k^2$ using ${k \choose 2}$. Then again for the leftover $k$ term. Now, if you sum the LHS, you sum the RHS. But by the stated thm, you can calculate the sum of the RHS.
Sep
25
comment General term of $(1+x)(1+x^2)(1+x^3)…$?
If you want to calculate these without calculating coeffs of the gf directly, I think the best formula is the recursive one in the OEIS: a(n)=(1/n)*Sum_{k=1..n} b(k)*a(n-k), with a(0)=1 and b(n)= A000593(n) = sum of odd divisors of n.
Sep
22
awarded  Good Answer
Sep
20
awarded  Nice Question
Sep
16
awarded  Yearling
Sep
10
awarded  Nice Answer
Sep
4
answered Proof of trigonometric identity $\cot \theta \sec\theta= 1/ \sin\theta$
Jul
31
awarded  Notable Question
Jul
28
comment Is every factorial divisible by its sum of digits?
@G.H.Faust: Add it to OEIS!!
Jul
27
comment Is every factorial divisible by its sum of digits?
what about sum of binary digits? (following the usual observation that there's nothing special about 10)
Jul
7
revised Converting recursive equations into matrices
typos
Jul
2
awarded  Curious
Jun
28
comment How to define the disciplines of mathematics
Everything is both similar and different from everything else. The general ideas of the above three categories solidify around their respective centers, but they cross over quite a bit.
Jun
6
comment 'Obvious' theorems that are actually false
For #4, the restriction where this _does work are given by the Fubini-Tonelli theorem
Jun
6
comment Why does differentiating a polynomial reduce its degree by $1$?
Nice... this is Sturm's theorem
Jun
6
comment Generalised Binomial Theorem Intuition
"why don't they teach it in secondary school?" - That's what math.SE is for.