|1/2-1|+|1/3-1/2|+1/4-1/3|+...|1/2009-1/2008|+|1/2010-1/2009|=?
问题描述:
|1/2-1|+|1/3-1/2|+1/4-1/3|+...|1/2009-1/2008|+|1/2010-1/2009|=?
答
原式=I1-1/2I+I1/2-1/3I+I1/3-1/4I+...I1/2009-1/2010I
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=2009/2010