High School Olympiads
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High School Olympiads
Regional, national, and international math olympiads
Regional, national, and international math olympiads
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Last Poster
Gaussian integral
soruz 3
N
Today at 8:25 AM
by Mathzeus1024
Exist a method of calculation for
, with help of
and Moivre's formula.


3 replies
Limit conundrum
MetaphysicalWukong 4
N
Today at 7:42 AM
by MetaphysicalWukong
Source: UNSW
Why is the last statement not true? And how do we know the selected option is true?
4 replies
Finding supremum of a weird function
pokoknyaakuimut 4
N
Today at 6:56 AM
by MihaiT
Find
. Easy to guess that the answer is
, but I haven't found the reason yet. :(


4 replies
Integration Bee Kaizo
Calcul8er 50
N
Yesterday at 7:10 PM
by Shikhar_
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
50 replies
Putnam 1950 B1
centslordm 2
N
Yesterday at 6:19 PM
by KAME06
In each of
houses on a straight street are one or more boys. At what point should all the boys meet so that the sum of the distances that they walk is as small as possible?

2 replies
Some integrals and sums(series)
Martin.s 1
N
Yesterday at 12:09 PM
by Entrepreneur
Source: Inspired from silver08
I saw Silver's post, so I thought I'd share some integrals and sums as well.
It's Christmas!!! (or boxing day.)








![\[
\text{Find: }
10. \sum_{n=1}^\infty \sum_{m=-\infty}^\infty \frac{1}{n^p m^2 (m^2 + 1)^3 (n+1)^q}, \quad 2 \leq p, q \in \mathbb{Z},
\]](//latex.artofproblemsolving.com/f/3/3/f3360b85ce092804a9de263cac49aed025ea8cee.png)
![\[
11. \sum_{n=1}^\infty \sum_{m=-\infty}^\infty \frac{(-1)^{n+m}}{n^p m^2 (m^2 + 1)^3 (n+1)^q}, \quad 2 \leq p, q \in \mathbb{Z}.
\]](//latex.artofproblemsolving.com/9/4/5/945aaa2340a4fb314e5eb218ba5286eb054c1b6f.png)
It's Christmas!!! (or boxing day.)








![\[
\text{Find: }
10. \sum_{n=1}^\infty \sum_{m=-\infty}^\infty \frac{1}{n^p m^2 (m^2 + 1)^3 (n+1)^q}, \quad 2 \leq p, q \in \mathbb{Z},
\]](http://latex.artofproblemsolving.com/f/3/3/f3360b85ce092804a9de263cac49aed025ea8cee.png)
![\[
11. \sum_{n=1}^\infty \sum_{m=-\infty}^\infty \frac{(-1)^{n+m}}{n^p m^2 (m^2 + 1)^3 (n+1)^q}, \quad 2 \leq p, q \in \mathbb{Z}.
\]](http://latex.artofproblemsolving.com/9/4/5/945aaa2340a4fb314e5eb218ba5286eb054c1b6f.png)
![\[12.
\int_{0}^{\frac{\pi}{4}} \frac{\sin x}{\cos(2x) + 2} \tan^{-1}\left(\frac{\cos x \cot(2x)}{\sqrt{2}}\right) dx
= \frac{5\pi^2}{48\sqrt{2}} - \frac{\pi}{4\sqrt{2}} \cos^{-1}\left(\frac{1}{3}\right).
\]](http://latex.artofproblemsolving.com/b/1/3/b13a5b1c537926c8323170d3d533b0bc71bb06a1.png)
1 reply
