In Latin, ad infinitum means to infinity. As a loan phrase in English, it sometimes means to infinity, but it’s usually used as an adverb meaning endlessly or without limit. As in the examples below, it usually follows the verb or verb phrase it modifies. Ad infinitum is well established in English, so it does not need to be italicized in normal use.
On Sunday, President Hugo Chavez won the right to seek reelection ad infinitum. [Los Angeles Times]
You go round in a circle ad infinitum; the trick is to make sure each new item fits into a story in your imagination. [Guardian]
Mistrust, violence, intimidation and psychological abuse will continue, ad infinitum, as West Papuans are pushed further aside. [Sydney Morning Herald]
[I]t is almost certain their backers are already planning the next round, in a process that will continue in one form or another ad infinitum. [Wired]