1/1*2=1-1/21/2*3=1/2-1/31/3*4=1/3-1/4.1/2009*2010=1/2009-1/2010所以 1/1*2+1/2*3+1/3*4············1/2009*2010=1-1/2+1/2-1/3+1/3-1/4+.+1/2009-1/2010=1-1/2010=2009/2010