有一组数1/2,1/6,1/12,1/20,.前20个数的和是多少

问题描述:

有一组数1/2,1/6,1/12,1/20,.前20个数的和是多少

1/(1*2)+1/(2*3)+1/(3*4)+.+1/(20*21)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/20-1/21)
=1-1/2+1/2-1/3+1/3-1/4+.+1/20-1/21
=1-1/21
=20/21