JERUSALEM — Palestinian Authority President Mahmoud Abbas formally announced Friday that the Palestinians will ask the U.N. Security Council next week to approve full membership of a Palestinian state in the United Nations. The announcement, in a speech to top Palestinian officials at Abbas’s office in Ramallah, appeared to seal the fate of last-ditch efforts by the Obama administration and other international mediators to come up with a formula to resume Israeli-Palestinian talks and head off the U.N.