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This is now fixed, so i am retagging this question from confirmed_bug to solved_bug:

sage: f(n) = (-1)^(n+1)/(3*n+6*(-1)^n)
sage: sum(f(2*n)+f(2*n+1),n,0,oo)
1/3*log(2) - 1/3

Thanks to all for making this happen !