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Mathematics
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Indecisive's user avatar
Indecisive's user avatar
Indecisive
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8
Compute $\sum^{2024}_{k=1} \frac{2023-2022 \cos \left(\frac{\pi(2k-1)}{2024} \right)}{2021-2020 \cos \left(\frac{\pi(2k-1)}{2024} \right)}$
Sep 25, 2023
7
Compute the largest natural number $n$ such that $2^n$ divides $S=\binom{2}{1}+\binom{4}{2}+\binom{8}{4}+\cdots+\binom{2^{100}}{2^{99}}$
Apr 14, 2023
5
Compute $\prod^{100}_{n=1} \left(5-4 \cos \left(\frac{\pi (2n-1)}{100} \right) \right)$.
Aug 26, 2023
5
Probability that a triangle inscribed in a square comprises at least $\frac{1}{4}$ of the area of the square
Mar 9
5
Reciprocals of positive integers in arithmetic progression
Jul 13
4
Find ratio formed by the perpendicular bisector of an angle bisector
Jul 3, 2023
3
Find $k>0$ such that $(k+1)+\sum^{\infty}_{n=1} \left(\frac{\binom{4n}{n}}{3n+1} k^{2n}+\frac{2\binom{4n+1}{n}}{3n+2} k^{2n+1} \right)=2$
Apr 17, 2023
3
Find ratio formed by intersection of segments in a triangle
Jul 29, 2023
3
Finding area of hexagon inscribed in rectangle
Jul 31, 2023
3
$I$ is the incenter of $ABC$. The extension of $AI$ meets the circumcircle of $ABC$ at $D$. If $AB=3$, $AC=4$, and $[IBC]=[DBC]$, find $BC$.
Feb 4