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:作业帮 时间:2024/06/30 11:35:18
![1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…+n) 的值 ,](/uploads/image/z/12476523-3-3.jpg?t=1%2F%281%2B2%29%2B1%2F%281%2B2%2B3%29%2B1%2F%281%2B2%2B3%2B4%29%2B%E2%80%A6%2B1%2F%281%2B2%2B3%2B4%2B%E2%80%A6%2Bn%29+%E7%9A%84%E5%80%BC+%2C)
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)