问题标题:
1/1X4+1/4X7+1/7X10+.+1/2002X2005=?有规律的
问题描述:
1/1X4+1/4X7+1/7X10+.+1/2002X2005=?
有规律的
冯京津回答:
1/1X4=(1/1-1/4)/3
1/4X7=(1/4-1/7)/3
...
1/2002X2005=(1/2002-1/2005)/3
1/1X4+1/4X7+1/7X10+.+1/2002X2005
=(1/1-1/4+1/4-1/7+...+1/2002-1/2005)/3
=(1-1/2005)/3
=668/2005