原式=1/(B-A) [(1/A -1/B) +1/(A-1)- 1/(B-1) +...+ 1/(A-2010) -1/雹盯(B-2010)]
将喊肆冲A,B的值代入可知: 1/(B-A)=1
则郑歼原式= -1/2+1 -1/3 +1/2 -1/4 +1/3 -1/5+1/4-.....-1/2012 +1/2011
=1- 1/2012
=2011/2012
1/AB+1/(A-银盯1)(B-1)+……1/(A-2010)(B-2010)
=1/1*2+1/2*3++……1/2012*2011
=1-1/2+1/悄搏空2-1/3+1/3-1/4+……+1/2011-1/启瞎2012
=1-1/2012=2011/2012
有点难
1