1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,b=-1)
问题描述：
1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,b=-1)
答
当a=-2,b=-1时
1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2011)(b-2011)
=1/[-2×(-1)]+1/[-3×(-2)]+1/[-4×(-3)]+……+1/[-2013×(-2012)]
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2012×2013)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
=1-1/2013
=2012/2013