MathDB

2

Part of 2012 China Western Mathematical Olympiad

Problems(2)

Isosceles triangles in regular polygon

Source: CWMO 2012 Q2

10/1/2012
Show that among any n≥3n\geq 3 vertices of a regular (2n−1)(2n-1)-gon we can find 33 of them forming an isosceles triangle.
geometrygeometric transformationreflection
Find integer

Source: China Western Mathematical Olympiad 2012 P6

9/29/2012
Define a sequence {an}\{a_n\} bya0=12, an+1=an+an22012,(n=0, 1, 2, ⋯ ),a_0=\frac{1}{2},\ a_{n+1}=a_{n}+\frac{a_{n}^2}{2012}, (n=0,\ 1,\ 2,\ \cdots), find integer kk such that ak<1<ak+1.a_{k}<1<a_{k+1}.
(September 29, 2012, Hohhot)
limitlogarithmsalgebra proposedalgebra