Induction question about triangle pattern Let n be a positive integer. An equilateral triangle is divided into $4^n$ equilateral congruent triangles and the top small triangle is cut off . Show that it can covered trapezoids formed by 3 of the small triangles.

I would start by proving the base case of $n=1$, which is clearly doable, assume $n=k$ is doable, and then prove that $n=k+1$ is also doable by showing that a triangle pattern of a smaller size can fit and the cut-off rearranged to form the trapezoid, showing that tiling it is possible. It doesn't seem that you can move the triangles and make the same case.
$$4^n - 1 = (4-1) (4^{n-1} + 4^{n-2} + \cdots + 4 + 1)$$

Each trapezoid contains $4-1$ triangle
$$4^n - 1 = (4-1) (4^{n-1} + 4^{n-2} + \cdots + 4 + 1)$$

Each trapezoid contains $4-1$ triangle