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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?
This is a bug. Please submit bug report to WRI (email: support@wolfram.com)