Proving bounds or convergence in sequences.
This problem is inspired by classic VMO analysis questions, which often bridge the gap between high school algebra and university-level calculus. Let a sequence be defined by Selected Problems of the Vietnamese Mathematica...
Unlike the shorter, high-speed AMC or AIME exams, the VMO often feels like a marathon. Problems are designed to test deep structural understanding rather than just "tricks." Vietnam has historically been a powerhouse in the International Mathematical Olympiad (IMO), and the VMO is the sieve that catches their finest analytical minds. Selected Problem: Sequences & Convergence Proving bounds or convergence in sequences
xn+1=xn+1⌊xn⌋x sub n plus 1 end-sub equals x sub n plus the fraction with numerator 1 and denominator the floor of x sub n end-floor end-fraction Problems are designed to test deep structural understanding
The Vietnamese Mathematical Olympiad (VMO) is legendary in the competitive math world for its grueling multi-day format and its penchant for "beautifully difficult" geometry and functional equations.