By means of the linearization method, we examine quasi balanced series \( \Omega _m \tiny { \begin{pmatrix} \begin{array}{cc|cc} \mu , & \nu \\ \lambda ,& \rho \end{array}&\varepsilon \end{pmatrix}}\) , containing five integers \(\{\mu ,\nu ,\lambda ,\rho ,\varepsilon \}\) subject to the condition \(\lambda -\mu -\nu +\rho \ge \varepsilon \ge 0\) . It is shown that this \(\Omega \) -series can always be expressed as a finitely linear combinations of the reduced series \(\Omega _m\tiny {\begin{pmatrix} \begin{array}{cc|cc} 0, & 0\\ 0,& 0 \end{array}&0 \end{pmatrix}}\) . Several novel closed summation formulae are highlighted as applications.
