1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,

来源：学生作业帮助网编辑：六六作业网时间：2024/11/25 21:45:47

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n)的值,1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n)的值,

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,
首先：1+2+3+4+…+n=n(n+1)/2
∴原式=2/(2*3)+2/(3*4)+2/(4*5)+…+2/(n(n+1))
=2(1/2-1/3+1/3-1/4+1/4-1/5+…+1/n-1/(n+1))
=2(1/2-1/(n+1))
=(n-1)/(n+1)