初中发现规律数学题

(-1*1/2) (-1/2*1/3) (-1/3*1/4) .......(-1/2009*1/2010) (-1/2010*1/2011)

因为因子的个数是偶数，所以乘积是正的。

=(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