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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Sequence
lgx57   1
N 36 minutes ago by lgx57
$a_1=1,a_{n+1}=a_n+\frac{1}{a_n}$. Find the general term of $\{a_n\}$.
1 reply
lgx57
37 minutes ago
lgx57
36 minutes ago
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20 fair coins are flipped, N of them land heads 2024 TMC AIME Mock #6
parmenides51   3
N 40 minutes ago by ostriches88
$20$ fair coins are flipped. If $N$ of them land heads, find the expected value of $N^2$.
3 replies
parmenides51
Yesterday at 8:05 PM
ostriches88
40 minutes ago
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Inequalities
sqing   10
N an hour ago by sqing
Let $ a,b \in [0 ,1] . $ Prove that
$$\frac{a}{ 1-ab+b }+\frac{b }{ 1-ab+a } \leq 2$$$$ \frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 }+\frac{ab }{2+ab } \leq 1$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+ab }\leq \frac{5}{2}$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+2ab }\leq \frac{7}{3}$$$$\frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 } +\frac{ab }{1+ab }\leq \frac{7}{6 }$$
10 replies
sqing
Apr 25, 2025
sqing
an hour ago
J
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Double Sum
P162008   1
N an hour ago by alexheinis
Evaluate $\Omega = \sum_{m=1}^{\infty} \sum_{n=0}^{m-1} \frac{(-1)^{m-n}}{(m^2 - n^2)^2}.$
1 reply
P162008
Yesterday at 9:55 AM
alexheinis
an hour ago
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shortest area bisector in right + isosceles (1994 Denmark MO - Mohr Contest p5)
parmenides51   0
Aug 18, 2020
In a right-angled and isosceles triangle, the two catheti are both length $1$. Find the length of the shortest line segment dividing the triangle into two figures with the same area, and specify the location of this line segment
0 replies
parmenides51
Aug 18, 2020
0 replies
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shortest area bisector in right + isosceles (1994 Denmark MO - Mohr Contest p5)
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parmenides51
#1 h  Aug 18, 2020, 7:36 PM
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In a right-angled and isosceles triangle, the two catheti are both length $1$. Find the length of the shortest line segment dividing the triangle into two figures with the same area, and specify the location of this line segment
This post has been edited 1 time. Last edited by parmenides51, Aug 18, 2020, 7:42 PM
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