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Magnetic properties of the non-uniform quantum Heisenberg spin chains with S = 1/2 are investigated using the transfer matrix renormalization group method. By analyzing the spin alignment in the two spin chains, we show the magnetic interaction mechanism for the dominant ferromagnetic behavior. For the moderate ferromagnetic coupling of the spin-1/2 ferromagnetic-ferromagnetic-antiferromagnetic Heisenberg chain, two maximums are found in the magnetic susceptibility from spin frustration. (c) 2005 Elsevier B.V. All rights reserved.