Back in the mid-aughts, Microsoft’s C.E.O. at the time, Steve Ballmer, flew to Palo Alto to try to convince Mark Zuckerberg, the young C.E.O. of Facebook, to let Microsoft buy his company. During Facebook’s first couple of years, bigger companies had dismissed it, and social networking in general, as a fad for college kids; Zuckerberg had even admitted that he didn’t care how Facebook would eventually make money. But Ballmer, who wanted to catch up to Google in the online-advertising business, was beginning to see Facebook’s power. People were signing up for accounts in extraordinary numbers.