It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant.We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions.Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter.One branch(the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero,in which case the effective cosmological constant becomes identical with the bare value,while the other(i.e.the "+") branch is singular in the same limit,and beyond this singular limit,the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.
