A collection of balls is stacked as follows. The top layer consists of 2 balls, the second layer consists of a 2 x 3 rectangular array of balls, the third a 3 x 4 array, etc. The balls in one row sit in the "dimples" in the row beneath. The first three layers are shown in the figure below:

- If there are 100 layers in the stack, what is the total number of balls?
- If each ball has a radius of 1 inch, how high is the stack?
- Can you generalize to the case where there is a 1 x
*n*rectangle of balls in the first row, a 2 x (*n*+1) rectangle in the second, etc., with a total of*m*layers?