We propose a simple pedagogical way of introducing the Euler–MacLaurin summation formula in an
undergraduate course on statistical mechanics. The reason is that the students may feel more
comfortable and confident if they are able to deduce the main equations. To this end we put forward
two alternative routes: the first one is the simplest and yields the first two terms of the
expansion. The second one is somewhat more elaborate and takes into account all the correction
terms. We apply both to the calculation of the simplest one-particle canonical partition functions
for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic
calculation of the correction terms is suitable for motivating the students to explore the
possibility of using available computer algebra software that enable one to avoid long and tedious
manipulation of algebraic equations.