1/1*2+1/2*3+1/3*4+......+1/1000*1001
来源:百度知道 编辑:UC知道 时间:2024/06/21 19:21:10
求简便算式
为什么,请详细说明
为什么,请详细说明
1/n(n+1)=1/n-1/(n+1)
原式=(1-1/2)+(1/2-1/3)+……+(1/1000-1/1001)
=1-1/1001
=1000/1001
1/[N*(N+1)]=1/N-1/(N+1)
所以,
原式
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+[1/N-1/(N+1)]
=1-1/(N+1)=N/(N+1)
=1000/1001
1-1/1001=1000/1001
1/1*2+1/2*3+1/3*4+......+1/1000*1001
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/1000-1/1001)]
=1-1/1001
=1000/1001
公式 1/M*N=1/M-1/N (M<N)
1/1*2+1/2*3+1/3*4+......+1/1000*1001=1-1/2+1/2-1/3+1/3-1/4…………+1/1000-1/1001=1-1/1001=1000/1001
1/1*2+1/2*3+1/3*4+......+1/1000*1001
=1-1/2+1/2-1/3+...+1/1000-1/1001
=1-1/1001
=1000/1001
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100
1-1/2+1/3-.....-1/10
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
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