Examples of mathematical induction What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ where the number of terms depends on $n$ and you're doing induction on $n$?
Postscript three years later: I see that I phrased this last part in a somewhat clunky way. I'll leave it there but rephrase it here:



--- that are not instances of induction on the number of terms in a sum?




Does proving statements like $f(n) \leq g(n)$ fit your bill? For instance, prove that $2^n \leq 2n!$.
