The tetrahedral numbers T1, T2, T3, . . . .Tk., . . . ., are the integers that count the n...

The tetrahedral numbers T1, T2, T3, . . . .Tk., . . . ., are the integers that count the number of dots on the faces of k nested tetrahedral, as shown in the following figure.

Show that the nth tetrahedral number is the sum of the first n triangular numbers.