若x＝1,y=2,求1／xy＋1／﹙x+1﹚·﹙y+1﹚＋1／﹙x＋2﹚·﹙y＋2﹚…………+1／﹙x+2009)·(y+2009)的值

题目

若x＝1,y=2,求1／xy＋1／﹙x+1﹚·﹙y+1﹚＋1／﹙x＋2﹚·﹙y＋2﹚…………+1／﹙x+2009)·(y+2009)的值

答案

1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+···+1/(x+2012)(y+2012)
=1/1x2+1/2x3+1/3x4+...+1/2013x2014
=1-1/2+1/2+1/3+1/3-1/4+...+1/2013-1/2014
=1-1/2014
=2013/2014