A pyramid of cubes is constructed as follows. The first (top) layer
contains one cube, the second layer contains three cubes, the third
layer contains six cubes, etc. The layers are configured as indicated
in the first figure and a picture of a pyramid with three layers is
shown in the second.
If we build a pyramid with 100 layers,
- how many cubes are in the bottom layer?
- what is the total number of cubes in the pyramid?