(Reuters) - Banks and miners propelled London's FTSE 100 to its best day in more than four months on Friday as optimism around the Sino-U.S. trade talks rose, but recent mixed signals on prospects of a deal still led the index to its worst week in two months.The main bourse advanced 1.4% with gains across the board, after slipping to a two-month low in the last session.The more domestically-focussed FTSE 250 rose 1.1% and bagged its sixth straight week of gains.U.S. President Donald Trump's..