1/1*2+1/2*3+1/3*4+.1/2000*2001

1/1*2+1/2*3+1/3*4+.1/2000*2001
=(1/1-1/2)+(1/2-1/3)+.+(1/2000-1/2001)
=1-1/2001
=2000/20011-1/2001？哪里没看懂？第二个等式1/1*2=1/2=1-(1/2)1/2*3=1/6=1/2-1/31/3*4=1/12=1/3-1/4这样把各项进行裂项分解