1/2,1/6,1/12,1/20前三十个数的和为什么

1/2+1/6+1/12+1/20+···+1/870+1/930=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+···+1/(29*30)+1/(30*31)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+···+(1/29-1/30)+(1/30-1/31)=1-1/2+1/2-1/3+1/3-1/4+1/4-1...