(1-1/2)+(1/2-1/3)+(1/3-1/4)+···+（1/2009-1/2010）根据等式关系,把括号去掉,原式变为1-1/2+1/2-1/3+1/3-1/4+···+1/2009-1/2010=1+（-1/2+1/2）+（-1/3+1/3）+···--1/2010括号内相加得0则=1-1/2010=2009/2...