Math Help - Induction Statements

I'm trying to find an example of a statement S(n) that is true for all natural numbers n but for which the assumption that S(k) is true from some k is not needed to show that S(k+1) is true.

Any ideas?

I guess you mean: It is not required to show S(0) and to show S(k) implies S(k+1).

Let S be:

n = n