1+1/1+2+1/1+2+3+...+1/1+2+3...+2000

来源：百度知道编辑：UC知道时间：2024/05/10 04:59:40

你好！

要用以下公式：
1+2+3+……+n=n(n+1)/2
1/(n(n+1))=(1/n)-(1/(n+1))

原式=2/(1×2)+2/(2×3)+2/(3×4)+……+2/(2000×2001)
=2×(1-1/2+1/2-1/3+1/3-1/4……+1/2000-1/2001)
=2×(1-1/2001)
=4000/2001

1+2+3+……+n=n(n+1)/2
1/(n(n+1))=(1/n)-(1/(n+1))

原式=2/(1×2)+2/(2×3)+2/(3×4)+……+2/(2000×2001)
=2×(1-1/2+1/2-1/3+1/3-1/4……+1/2000-1/2001)
=2×(1-1/2001)
=4000/2001

题目好像看不怎么懂,1/1什么意思?不就是1么?

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1+1/1+2+1/1+2+3.........+1/1+2+3.....100 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) 1+1/2+1+1/3+1+1/4+......+1/100=? (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2)