The second principle of mathematical induction
To show that P(n) is true for every positive integer n, show that:
Basis step. P(1) is true.
Inductive step. For every positive integer n, if P(1), P(2), …, P(n) are
Generalization: To show that P(n) is true for every integer n with n?k
(where k can be any integer, including 0 or negative integers), it suffices
1. Basis step: P(k) is true;
2. Inductive step: For every integer n with n?k, if P(k), P(k+1), …,
P(n) are true, then so is P(n+1).