观察下列各式发现规律计算下题原式：-1*1/2=-1+1/2；-1/2*1/3=-1/2+1/3等等以此推类.要计算的：

通过分析前三个算式可推出规律为：-1n×1n+1=-1n+1n+1；
(1*1/2)+(-1/2*1/3)+(-1/3*1/4)+…+（-1/2007*1/2008）+（-1/2008*1/2009）
=-1+1/2+(-1/2)+1/3+(-1/3)+1/4+…+（-1/2007）+1/2008（-1/2008）+1/2009
=-1+1/2-1/2+1/3-1/3+1/4-1/4…-1/2007+1/2008-1/2008+1/2009
=-1+1/2009
=-2008/2009