On the other hand, the overall accuracy of bound state computations achieved for three-electron atoms and ions is still substantially lower than analogous accuracy known for two-electron atomic systems. Therefore, the development of new, rapidly converging variational expansions and effective, fast computational methods is of paramount importance for the future of highly accurate calculations of three-electron atoms and ions. Third, despite a rapidly increasing stream of computational publications on three-electron atomic systems some fundamental aspects of such systems have not been discussed yet. For instance, the quality of the wave function constructed for an arbitrary Coulomb few- and many-body system can be tested by comparing the computed and expected cusp values, or cusps, for short. However, it appears that neither the electron-nucleus, nor electron-electron cusps were ever determined for three-electron atoms and ions. Another well known problem is related to an incorrect definition of some electron-nucleus and electron-electron properties accepted in quite a few earlier works performed for three-electron atoms and ions. Furthermore, it was found that the expectation values of some bound state properties computed with the use of different variational expansions deviate from each other. In a few cases such deviations are relatively large and may lead to 