数学计算:

来源：百度知道 编辑：UC知道 时间：2024/05/19 07:00:35
1/6+1/12+1/20+1/30+..........+1/2007*2008
=
=
=

1/6+1/12+1/20+1/30+..........+1/2007*2008
=1/2*3+1/3*4+1/4*5+1/5*6+......+1/2007*2008
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+......+1/2007-1/2008
=1003/2008

原式等于1\2-1\3+1\3-1\4+......+1\2007-1\2008 将中间的消掉 得到1\2-1\2008=1003\2008

1/6+1/12+1/20+1/30+..........+1/2007*2008
=1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2007*2008)
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+...+(1/2007)-(1/2008)
=(1/2)-(1/2008)
=1003/2008.