1/2+1/6+1/12+1/20+1/30······+1/90+1/110=( )

来源：学生作业帮助网编辑：六六作业网时间：2024/07/04 17:37:59

1/2+1/6+1/12+1/20+1/30······+1/90+1/110=()1/2+1/6+1/12+1/20+1/30······+1/90+1/110=()1/2+1/6+1/12+1/2

1/2+1/6+1/12+1/20+1/30······+1/90+1/110=( )
1/2+1/6+1/12+1/20+1/30······+1/90+1/110=( )

1/2+1/6+1/12+1/20+1/30······+1/90+1/110=( )
1/2 = 1/1*2 = 1/1-1/2
1/6 =1/2*3 = 1/2-1/3
1/12 = 1/3*4 = 1/3-1/4
.
1/90 = 1/9*10 = 1/9 - 1/10
1/110 = 1/10*11 = 1/10 -1/11
所以原式=1/1-1/2+1/2-1/3+1/3.-1/9+1/9-1/10+1/10-1/11=1-1/11=10/11

1-1/2+1/2-3/1+1/3-1/4。。。。。。。。。。。。。1/10-1/11=你懂得