I know Hume argued against dividing finite space into infinitely many regions, but I can't seem to find anything regarding his thoughts on infinity itself. From his Enquiry you sort of get that he thinks it is not productive to talk about the infinite generally speaking, but he doesn't explicitly say he is against it as far as I can tell.
I am interested in this as I am trying to make sense of his concept of infinity. In sections 2-3-4 of the above mentioned work, he says that we are free to combine however many simpler ideas and form more complex ones. He also says that The most lively thought is still inferior to the dullest sensation. This would suggest to me that, in his view, you could add up infinitely many low-vivacity parts (he says that thoughts and ideas are less vivacious, therefore they must have some vivacity) and the result would still be duller than the dullest first hand sensation. In order for this weird airthmetic of vivacity to make sense, one must have a different understanding of infinity.