Growing Ls


This is a size 1 L:


Four of them can be used to tile a size 2 L:

size 2 triomino tiled

 
Devise a convincing argument that you will be able to tile a size 4, 8, 16, 32... $2^n$ L using size 1 Ls.

  
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.