lean_workbook_plus_64280

Prove that at least one among $a_{1},a_{2},a_{3},...,a_{n}$ is less than $1$ given $a_{1}+a_{2}+a_{3}+...+a_{n}<n$ for positive real numbers $a_{1},a_{2},a_{3},...,a_{n}$ and a positive integer $n$.