1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+50)的解法

来源：学生作业帮助网编辑：作业帮时间：2024/05/08 22:55:54

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+50)的解法
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+50)的解法

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+50)的解法
1/(1+2+3+----+n)=1/[n(n+1)/2]=2[1/n-1/(n+1)]
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+50)
=2(1/2-1/3+1/3-1/4+1/4-1/5+-----+1/50-1/51)(消去中间部分)
=2(1/2-1/51)
=49/51