Issue with Sum of Floors in Mathematica

Question

I'm using Mathematica 8. When I try the command

Sum[r^n Floor[n/2], {n, 0, Infinity}]

I get

r^2/((-1 + r)^2 (1 + r)) 

which is correct, but starting from 1 instead of 0:

Sum[r^n Floor[n/2], {n, 1, Infinity}]

gives

r/((-1 + r)^2 (1 + r))

which is not. What's going on?

Answer 1

This is a bug. Please submit bug report to WRI (email: [email protected])