1/n(n+1)=1/n-1/(n+1)证明：右边=[(n+1)-n]/n(n+1）=1/n(n+1)=左边所以原式成立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中间全部消掉=1-1/2010=2009/2010
