Daf Yomi Nedarim 39b: His Illness Converges Towards Zero

Nedarim 39b, translation from my Rif blog:

ת"ר) ר' אחא ב"ר חנינא אומר כל המבקר את החולה נוטל אחד מששים מצערו
א"ל אביי א"כ לעיילו שתין ולוקמוהו
א"ל כעישורייתא דבי רבי ובבן גילו

(* The Sages learnt {in a brayta} *) R' Acha {our gemara: Abba} son of R' Chanina says: Anyone who visits a sill person takes away 1/60th of his suffering.
Abaye said {our gemara does not attribute this to Abaye}: If so, let 60 people enter and restore him!
He said to him: This is like the tenth of the house of Rabbi, and specifically someone of the same age {or under the same planetary influence}.
{in which each takes 1/60th of the remainder}

With the original assumption, if each took away 1/60th of the total, after 60 people, there would be no more illness, or else no more tzaar, left.

But even if one each one took 1/60th of the remainder, this would seem to be quite effective. With a quick calculation in Excel (put 100 in A1, in cell A2 type the formula =A1-(1/60)*A1, and then drag that formula down), we can see that after 60 visitors, the sick person would have only 36.5% left. After 100 visitors, he would have only 18.6% left. After 137 visitors, he would only have 10% left. After 200 visitors, he would have only 3.4% left. And finally, after 244 visitors, he would have 1.66% left, which is 1/60th of his illness. He would get to 1% of his illness after 274 visitors.

It will never reach 0, but it certainly converges towards that. And thus stands up to this numeric reduction. So why does the gemara not enter this rejoinder?

Perhaps it does, in also adding "and with his ben gilo," thus talking about a difficult situation to engineer. Perhaps that is what compelled it, rather than it being an alternate rejoinder.