  We discuss an approach to accurate numerical computations of slowly
convergent properties in two-electron atoms/ions which include the negatively
charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively
charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are
considered in their ground $1^{1}S-$state(s). The slowly convergent properties
selected in this study include the electron-nulceus $\langle r^{2 k}_{eN}
\rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation
values for $k$ = 2, 3, 4 and 5.
