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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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interesting integral
Martin.s   1
N 2 hours ago by ysharifi
$$\int_0^\infty \frac{\sinh(t)}{t \cosh^3(t)} dt$$
1 reply
Martin.s
Yesterday at 3:12 PM
ysharifi
2 hours ago
J
H
Two times derivable real function
Valentin Vornicu   10
N 3 hours ago by Rohit-2006
Source: RMO 2008, 11th Grade, Problem 3
Let $ f: \mathbb R \to \mathbb R$ be a function, two times derivable on $ \mathbb R$ for which there exist $ c\in\mathbb R$ such that
\[ \frac { f(b)-f(a) }{b-a} \neq f'(c) ,\] for all $ a\neq b \in \mathbb R$.

Prove that $ f''(c)=0$.
10 replies
Valentin Vornicu
Apr 30, 2008
Rohit-2006
3 hours ago
J
H
Find the volume of the solid
r02246013   3
N 5 hours ago by Mathzeus1024
Find the volume of the solid bounded by the graphs of $z=\sqrt{x^2+y^2}$, $z=0$ and $x^2+y^2=25$.
3 replies
r02246013
Dec 16, 2017
Mathzeus1024
5 hours ago
J
H
Find the greatest possible value of the expression
BEHZOD_UZ   0
5 hours ago
Source: Yandex Uzbekistan Coding and Math Contest 2025
Let $a, b, c, d$ be complex numbers with $|a| \le 1, |b| \le 1, |c| \le 1, |d| \le 1$. Find the greatest possible value of the expression $$|ac+ad+bc-bd|.$$
0 replies
BEHZOD_UZ
5 hours ago
0 replies
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Infinite series involving tau function
bakkune   1
N Apr 13, 2025 by Safal
For each positive integer $n$, let $\tau(n)$ be the number of positive divisors of $n$. Evaluate
$$ \sum_{n=1}^{+\infty} (-1)^n \frac{\tau(n)}{n} $$
1 reply
bakkune
Apr 13, 2025
Safal
Apr 13, 2025
J
Infinite series involving tau function
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Reveal topic tags
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divisor
infinite series
tau function
calculus
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bakkune
42 posts
bakkune
#1 h  Apr 13, 2025, 4:35 AM
Y by
For each positive integer $n$, let $\tau(n)$ be the number of positive divisors of $n$. Evaluate
$$ \sum_{n=1}^{+\infty} (-1)^n \frac{\tau(n)}{n} $$
This post has been edited 1 time. Last edited by bakkune, Apr 13, 2025, 4:36 AM
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Safal
168 posts
Safal
#2 h  Apr 13, 2025, 8:21 AM • 1 Y
Y by bakkune
Solution, hope you can finish the rest, the hard parts are done.
This post has been edited 7 times. Last edited by Safal, Apr 14, 2025, 4:44 AM
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