(-1*1/2) (-1/2*1/3) (-1/3*1/4) .(-1/2009*1/2010) (-1/2010*1/2011)
因为因数的个数为偶数,则积为正数
=(1*1/2) (1/2*1/3) (1/3*1/4) .(1/2009*1/2010) (1/2010*1/2011)
= 1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011】
= 1-1/2011
= 2010/2011