MYTS 2019 - Grade 8 - Round 2 Question 3

Numbers $a_1,a_2,\ldots,a_{2019}$ have sum greater than 1. Prove that some positive integer $n\le2019$ has the property that $a_n$, $a_n+a_{n-1}$, ..., $a_n+a_{n-1}+\cdots+a_1$ are all positive.