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The Euler-Poincar\'e characteristic of a finite-dimensional Lie algebravanishes. If we want to extend this result to Lie superalgebras, we should dealwith infinite sums. We observe that a suitable method of summation, which goesback to Euler, allows to do that, to a certain degree. The mathematics behindit is simple, we just glue the pieces of elementary homological algebra,first-year calculus and pedestrian combinatorics together, and present them ina (hopefully) coherent manner.

How Euler would compute the Euler-Poincar\'e characteristic of a Lie superalgebra