1/1乘2+1/2乘3+1/3乘4+1/4乘5+...+1/2009乘2010 你的意思是不是1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2009*2010)啊?1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2009*2010) =1/1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010 =1-1/2010 =2...