Let $a_0,a_1,\ldots$ be an infinite sequence of positive numbers. Prove that the inequality $1+a_n>\sqrt[n]2a_{n-1}$ holds for infinitely many positive integers $n$.
Source: Mongolian MO 2002 Grade 10 P5
Tags: inequalities, Sequence
Let $a_0,a_1,\ldots$ be an infinite sequence of positive numbers. Prove that the inequality $1+a_n>\sqrt[n]2a_{n-1}$ holds for infinitely many positive integers $n$.
