lean_workbook_plus_40279

Prove that for all real numbers $a_{1} , a_{2} , ... , a_{n}$ where $a_i$ are distinct and $n>1$, the following equation holds: $\frac{1}{(a_{1}-a_{2})(a_{1}-a_{3})...(a_{1}-a_{n})}+\frac{1}{(a_{2}-a_{1})(a_{2}-a_{3})...(a_{2}-a_{n})}+...+\frac{1}{(a_{n}-a_{1})(a_{n}-a_{2})...(a_{n}-a_{n-1})} = 0$