Falafel is the way

It is possible to monotonically increase and asymptotically approach a fixed boundary.

However, in real life you can't increase the amount of meat in a portion less than some amount of atoms, probably a cell is the smallest unit of meat, so we'll go with adding 1 cell of meat each kebab.

The smallest animal cell is apparently the sperm cell, but I don't think anon wants his kebab made with increasing amounts of animal jizz, so we'll instead go with muscle fibres instead.

According to scientists, there's around 630-ish Mt of domesticated animals on earth (eyeballing their python notebook). I'm pretty sure that includes cats/dogs/rats, but it's that or we measure with sperm on the kebab. Let's say the yield of meat is 50%, that's 275 Mt = 275e6 grams.

Apparently 1cm of meat is around ~1e7 cells (this is the weakest number in the analysis), so we have 275e6*1e7=2.75×10e15 total cells to distribute onto anon's kebabs.

Each kebab we have to add 1 more cell than the prior kebab (1 on day 1, 2 on day 2, and so on). The total number of cells consumed on kebab N is a triangle number, N * (N + 1) / 2, which we can solve to 74,161,984 kebabs. After which, there's simply not enough meat to make the remaining kebab.

Now, if we go back to the sperm example, I'm sure that could be renewably farmed, but the problem grows linearly in nature still.