Hi, and several googols of thanks for your help. When I tried your
vsum(n copies of x) = 1-2/(2*AT(x))^n
it did not work for me, probably due to a misunderstanding on my part. But your
vsum(n copies of x) = T(n*AT(x))
worked perfectly on my Haxial calculator, reproducing results identical to my own tedious calculations, eg: with n = 5, 10 and 50, using recursive versions of SR's original relation. Using your relation and pushing n to 10^7 and then 10^9, it also shows that vsum(n copies of x) converges quickly to
v = .761594155... Co,
instead of Co itself. This is unexpected, though I already knew that for n = 2, 3, 5 and 10 (with v = Co/2 , Co/3 , Co/5 and Co/10 ), the resultant velocities <decreased>, ie:
0.8 , 0.777 , 0..7672 and 0.76299 times Co ,
respectively (where Co = unity). This bothered me, especially since initially it seemed conceivable that the sum might even converge to 0.0 as n --> infinity and v --> 0.0 Co! Nevertheless, the actual con- vergence is still counter-intuitive, having expected the sum to rise eventually to Co, as I'm guessing you did too.
Interesting...though what it might mean physically is anybody's guess, without a ouiji board and Prof. Einstein.