The population will continue to grow for a while because of developing countries' life expectancy catching up with developed countries, but unless there are drastic technological breakthroughs to improve life expectancy beyond where developed countries are now, the world population will stop growing fairly soon.
Even if "children per person" falls slow enough you could even indefinitely increase the rate that new people are added right?
https://commons.wikimedia.org/wiki/File:World_population_(UN...
(Interestingly, the above chart was created about 10 years ago; I do wonder how accurate it's been.)
All I meant to point out is that "birth rate falling" doesn't map to "population falling", if the average number of children per couple drops 2.5 to 2.1 then each generation is still larger (and the population still grows exponentially).