x1=1
x2=2
x3=3
……
1/1*3+1/2*4+1/3*5+1/4*6+…+1/2008*2010+1/2009*2011
=1/1*3+1/3*5+1/5*7+…+1/2009*2011+1/2*4+1/4*6+1/6*8+…1/2008*2010
=（1-1/3+1/3-1/5+1/5-…+1/2009-1/2011+1/2-1/4+1/4-1/6+1/6-…+1/2008-1/2010）×1/2
=（1-1/2011+1/2-1/2010）×1/2 中间的被抵消了
=（2010/2011+1004/2010）×1/2
=6059144/4042110×1/2
=3029572/4042110
=1514786/2021055