MathDB

2

Part of 2020 Malaysia IMONST 2

Problems(2)

Malaysia IMONST 2 Senior Problem 2

Source: Malaysia IMO national selection test 2020

10/19/2020
Prove that 1−12+13−14+⋯+12019−12020=11011+11012+⋯+120201-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots +\frac{1}{2019}-\frac{1}{2020}=\frac{1}{1011}+\frac{1}{1012}+\cdots +\frac{1}{2020}
algebraFractions
every equilateral triangle can be divided into n>=6 equilateral triangles.

Source: 2020 Malaysia IMONST Round 2 Junior 2

9/22/2021
Prove that for any integer n≥6n\ge 6 we can divide an equilateral triangle completely into nn smaller equilateral triangles.
geometrycombinatorial geometrycombinatoricsequilateralsEquilateral