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As a continuation of Parts I \cite{Part-1:2020}, II \cite{Part-2:2021}, III\cite{Part-3:2022}, where ultra-compact wave functions were constructed for afew low-lying states of He-like and Li-like sequences, the family ofspin-singlet $(1s\,ns)$ type excited states $n\,{}^1 S$ of the He-like sequenceis studied with an emphasis on the $n=3,4,5$: $3\,{}^1 S, 4\,{}^1 S, 5\,{}^1 S$states, for nuclear charges $Z \leq 20$. Particular attention is given tofinding of critical charges $Z=Z_B$ at which the ultra-compact wave functionslose their square-integrability.  For each ${}^1 S$ state an ultra-compact, seven-parametric trial function isconstructed, which describes the domain of applicability of thenon-relativistic Quantum Mechanics of Coulomb Charges (QMCC) for the totalenergies (4-5 significant digits (s.d.)) and reproduces 3 decimal digits (d.d.)of the spin-singlet states $n\,{}^1 S$ of He-like ions (in the staticapproximation with point-like, infinitely heavy nuclei) for $n=1,2,3,\ldots$and any $Z \leq 20$\,. All energies are well described by second degreepolynomials in $Z$ (the Majorana formula).  Critical charges $Z=Z_B^{(n)}$, where the ultra-compact trial function forthe $n^1 S, n=1,2,3,\ldots$ states loses its square-integrability, areestimated: for all studied states $Z_B^{(n)}$ increases slowly with $n$; itseems they lie in the interval $Z_B(n^1 S) \sim 0.90 - 0.95$, in particular,with $Z_B^{(1)}=Z_B^{(2)}\,=\,0.904$, $Z_B^{(3)}=Z_B^{(4)}\,=\,0.928$,$Z_B^{(5)}\ =\ 0.939$.

Ultra-Compact accurate wave functions for He-like iso-electronic  sequences and variational calculus. IV. Spin-singlet states $(1s\,ns)$  $n\,{}^1 S$ family of the Helium sequence