In this note we introduce an infinite series which represents an interesting challenge for students with the relevant background.

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

In this note, the author considers a class of infinite series and shows that these are equivalent to a number of definite integrals, some of which are improper integrals. By using Taylor's theorem in this equivalence the author establishes convergence of each series, and a means of evaluating the sum of the series and the definite integral to any…