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We obtain the phase diagram in the parameter space $(J'/J, \gamma)$ and anaccurate estimate of the critical line separating the different phases. We showseveral measuments of the magnetization, dimerization, nearest neighbourscorrelation, and density of energy in the different zones of the phase diagram,as well as a measurement of the string order parameter proposed as the nonvanishing phase order parameter characterizing Haldane phases. All theseresults will be compared in the limit $J'/J\gg 1$ with the behaviour of the$\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of ourdata supports the existence of a dimer phase separated by a critical line froma Haldane one, which has exactly the same nature as the Haldane phase in the$\textbf{S}=1$ BAHC.

DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings