Prove that 1 plus 2 plus ... plus n equals n times (n plus 1) divided by 2, using induction. Base case n equals 1: left side is 1, right side is 1 times 2 divided by 2 equals 1, true. Inductive step: assume the formula holds for n. For n plus 1, the sum is the old sum plus (n plus 1), which by assumption equals n(n+1)/2 plus (n+1). Factoring (n+1) gives (n+1)(n+2)/2, exactly the formula for n plus 1. The base knocks the first domino; the step knocks each next domino from any standing one.