Ok, so I have a function that will give probability for any single die roll:

Code:

function probability(a){
var b = Math.abs(a -3.5)+.5;
return Math.pow(6,-Math.ceil(b/3))/ (b%3==0?2:1);
}

Yes, its steps up in series of three, going outwards from the 3-4 center, with the third element being half the value of the other two, and each set of three decreasing in likelihood by 6.

Now we can deal with that infinite series you lined up for us to calculate...