2. Methodology
Usually, mathematical induction is included in the last grades curriculum of secondary school. However,
preliminary steps in its main idea learning are possible to be exercised earlier by means of a computer. It is not
meant a full induction but small inductive steps that lead students to knowledge. The authors propose an approach,
which is similar to the so called Socratic style getting the truth via inquiry. The original Socratic method is not
advocated here, because it is not used a questioning to dismantle or discard preexisting ideas. It is emphasized only
on the ultimate goal of such a style – to increase understanding through inductive steps. Induction is a hidden reality
of science and the computer is a convenient tool to reveal a part of it or at least to give a possibility of investigating
to a level, which supports its full study. The induction method could be realized as an experimental approach to a
given mathematical problem. This approximates the problem to one from the domain of the experimental science, by
which a mathematical relation is discovered. Well-known arithmetic formulae are derived in the sequel and some
applications are proposed.
The following formulae for arbitrary positive integers n are attacked by mathematical induction, usually: