odd numbers is equal to
however great
may be. When a general law of this sort is established, we can apply its formula to any particular case and thus obtain a solution without further ado.
The procedure whereby this law is obtained is that of mathematical Induction. We verify the fact that the sum of the first two odd numbers is
; then we prove that if this is the case, the sum of the first three odd lumbers must necessarily be 32. Finally, we prove that if the sum of the first (
