If n is Triangular then so is 9n + 1

Theorem
Let $$n$$ be a triangular number.

Then $$9 n + 1$$ is also triangular.

Proof
Let $$n$$ be triangular.

Then $$\exists k \in \Z: n = \frac {k \left({k+1}\right)} 2$$.

So:

$$ $$ $$

which is triangular.