1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
.
1/n(n+1)=1/n-1/(n+1)
1/1*2+1/2*3+1/3*4+．．．．1n（n＋1）
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+[1/n-1/(n+1)]
=1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)