1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 04:01:37
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)=?

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)=?
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)=?

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)=?
1/(1+2+3+……+n)=1/[n(n+1)/2]=2/[n(n+1)]
=2*[1/n-1/(n+1)]
所以1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.1/(1+2+3+4+5+6+.+50)
=2*[(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/50-1/51)]
=2*(1-1/51)
=100/51