1/1*2*3+1/2*3*4+1/3*4*5 省略 1/98*99*100

问题描述:

1/1*2*3+1/2*3*4+1/3*4*5 省略 1/98*99*100
*是乘号
要最简便的,这个好象有点复杂!

1/1*2*3+1/2*3*4+1/3*4*5 +.+1/98*99*100=1/2*[2/(1*2*3)+2/(2*3*4)+...+2/(98*99*100)] =1/2*[(3-1)/(1*2*3)+(4-2)/(2*3*4)+...+(100-98)/(98*99*100)] =1/2*[3/(1*2*3)-1/(1*2*3)+4/(2*3*4)-2/(2*3...