Will ants eventually go away if you keep killing them?

No, ants will not eventually go away if you keep killing only the visible workers you see, because killing individual foragers does not eliminate the colony, queen, or nest that contains thousands of members hidden in walls, under floors, or outdoors, and can actually make the infestation persist longer and spread. Odorous house ants, which are tiny black ants common in kitchens, have colonies with thousands of workers and a queen that can live 3 to 7 years and continuously lay eggs, so when you kill a few hundred foragers, the queen simply produces more workers to replace them, and new ants will continue following pheromone trails to food as long as crumbs, sweets, grease, and moisture remain available and entry points are open. Worse, squishing odorous house ants releases alarm pheromones and oleic acid that attract more ants to investigate and can cause budding where surviving ants split into satellite colonies in other parts of your house, leading to more trails elsewhere rather than fewer. Killing foragers also does not erase the chemical trails that guide ants, so new recruits will follow the same paths. To make ants eventually go away permanently, you need to eliminate the entire colony including the queen using slow-acting gel baits containing fipronil, hydramethylnon, or borax such as Terro Liquid Ant Bait placed near trails, allowing workers to carry bait back through trophallaxis to kill queen within days to two weeks, combined with sanitation by storing food sealed and cleaning crumbs, sealing cracks with caulk, and fixing moisture issues for carpenter ants.