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To solve the cosmological constant fine tuning problem,we investigate an (n+1)-dimensional general-ized Randall-Sundrum brane world scenario with two (n- 1)-branes instead of two 3-branes.Adopting an anisotrop-ic metric ansatz,we obtain the positive effective cosmological constant Ωeff of order 10-124 and only require a solu-tion (≌) 50-80.Meanwhile,both the visible and hidden branes are stable because their tensions are positive.There-fore,the fine tuning problem can be solved quite well.Furthermore,the Hubble parameter H1 (z) as a function of red-shift z is in good agreement with the cosmic chronometers dataset.The evolution of the universe naturally shifts from deceleration to acceleration.This suggests that the evolution of the universe is intrinsically an extra-dimensional phe-nomenon.It can be regarded as a dynamic model of dark energy that is driven by the evolution of the extra dimen-sions on the brane.