$\sum_{n=1}^{\infty}\frac{1}{4^n}=\frac 13$ geometrically

Question

As $$\sum_{n=1}^{\infty}\frac{1}{4^n}$$ is a geometric series it is not hard to see that the result is $\frac 13$.

But how can this be seen by the following picture?

Answer 1

The big grey triangle is $\frac14$ of the big white, the second grey is $\frac14$ of the top white $\frac14$, etc.

On the other hand, the grey part is certainly $\frac13$ of all because we can combine each grey with the same-size white triangles to its left and right and these trapezoids tile the whole.