MathDB

Problem 5

Part of 2002 Mongolian Mathematical Olympiad

Problems(2)

inequality in sequences

Source: Mongolian MO 2002 Grade 10 P5

4/9/2021
Let a0,a1,…a_0,a_1,\ldots be an infinite sequence of positive numbers. Prove that the inequality 1+an>2nan−11+a_n>\sqrt[n]2a_{n-1} holds for infinitely many positive integers nn.
inequalitiesSequence
cyclic pentagon, ratio of product of sides to diagonals

Source: Mongolian MO 2002 Teachers P5

4/9/2021
Let AA be the ratio of the product of sides to the product of diagonals in a circumscribed pentagon. Find the maximum possible value of AA.
ratiogeometry