1/(120)+1/(23)+1/(34).+1/(20092010)=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/08 04:38:08

1/(1*20)+1/(2*3)+1/(3*4).+1/(2009*2010)=?
1/(1*20)+1/(2*3)+1/(3*4).+1/(2009*2010)=?

1/(1*20)+1/(2*3)+1/(3*4).+1/(2009*2010)=?
1/(1*2)+1/(2*3)+1/(3*4).+1/(2009*2010)
=[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2009-1/2010)]
=(1-1/2010)
=2009/2010

1/(1*2)+1/(2*3)+1/(3*4)....+1/(2009*2010)
=1-1/2+1/2-1/3+1/3-1/4…+1/2009-1/2010
=1-1/2010
=2009/2010
(“/”表示分数线）