1/2*3=1/2-1/3
1/3*4 =1/3-1/4
以此类推,
1/2008*2009 =1//2008-1/2009
所以原式可化为:
1/1*2+(1/2-1/3)+(1/3-1/4)+……+1/2008-1/2009
去括号后显然等于1-1/2009=2008/2009
1/2*3=1/2-1/3
1/3*4 =1/3-1/4
以此类推,
1/2008*2009 =1//2008-1/2009
所以原式可化为:
1/1*2+(1/2-1/3)+(1/3-1/4)+……+1/2008-1/2009
去括号后显然等于1-1/2009=2008/2009