Repunit in base nine

Statement

Convert $1111_{9}$ (all digits equal to $1$) to base ten and check that it is a triangular number.

Solution

$1111_{9}=9^3+9^2+9+1=729+81+9+1=\boxed{820}.$ Moreover $820=T_{40}=\dfrac{40\cdot 41}{2}$: in base $9$ every number made of only $1$‘s is triangular.