Hi Steve, in case you still care, the geometric mean using just the return, 'R', won't work out the the same as 1+R, in theory or practice.

Try returns of 10%, 20%, and 30% (geomean is in Excel )
geomean(.1, .2, .3) ~= 0.182
geomean(1.1, 1.2, 1.3)-1 ~= 0.197, or 19.7%

Apply to an $100 investment over 3 periods:
$100 *1.1*1.2*1.3 = $172
$100*1.197*1.197*1.197 =$172
1.182 (or 0.182 for that matter) would not get you the right number.

Now, if you're seeing people calculating the arithmetic mean of positive returns for a different purpose, then it doesn't matter, you don't have to add the 1.