题目写错了吧,应该是1/[a(a+1)]+1/[(a+1)(a+2)]+...+1/[(a+2009)(a+2010)]原式=[(a+1)-a]/[a(a+1)]+[(a+2)-(a+1)]/[(a+1)(a+2)]+...+[(a+2010)-(a+2009)]/[(a+2009)(a+2010)]=[1/a-1/(a+1)]+[1/(a+1)-1/(a+2)]+...+[...