1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2009)=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 08:18:41
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2009)=?1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2009)=?
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2009)=?

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/(2007*2008*2009)=?
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6
=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+1/2*(1/4/5-1/5*6)
=1/2*(1/1*2-1/5*6)
=7/30