(1-1/毕袜2-1/3-...-1/2008)×(1/2+1/3+1/4+...+1/2009)-(1-1/2-1/3-...-1/2009)×(1/2+1/3+1/手侍激4+...+1/2008)令1-1/2-1/3-...-1/2008=a1/2+1/3+1/4+...+1/2008=ba+b=1则原式可化谈拍为a×(b+1/2009)-(a-1/2009)×b=a×b+a/2009-a×b+b/2009=(a+b)/2009=1/2009