Verify Theorem 4.2.
The Principle of Mathematical Induction-Alternative Form. Let S(n) denote an open mathematical statement (or set of such open statements) that involves one or more occurrences of the variable n, which represents a positive integer. Also let no, n\ e Z+ with n0 < n1.
a) If S(n0), S(n0 + 1), S(n0 + 2), . . ., S(n1 - 1), and S(n1) are true; and
b) If whenever S(n0), S(n0 + 1),..., S(k - 1), and S(k) are true for some (particular but arbitrarily chosen) k ∈ Z+, where k > n1, then the statement S(k + 1) is also true;
then S(n) is true for all n > n0.