NEW YORK (Reuters) - Warren Buffett's Berkshire Hathaway Inc will pay $26 billion to buy out Burlington Northern Santa Fe Corp in a bet the nation's largest rail company will benefit from a recovering U.S. economy. The deal, announced on Tuesday, is the billionaire investor's biggest-ever acquisition and may prompt him to sell some of his other investments, which include a wide range of companies from Coca-Cola Co to General Electric Co, some Buffett watchers said. By betting on BNSF, Buffett -- the world's second-richest person and a long-time model train buff -- renewed interest in a storied, but highly cyclical American industry that has tried to reinvent itself by emphasizing its ability to move goods cheaply and efficiently. "It's an...