规律探索:1/1x2=1/1-1/2;1/2x3=?;1/3x4=?;1/n(n+1)=?根据以上规律计算:1/1x2+

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