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(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)

来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/10 10:21:05
(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕
(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)
quickly
(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
=1+2(1/2-1/3+1/3-1/4+...+1/1000-1/1001)
=1+2(1/2-1/1001)
=2000/1001
(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1))
=1/3(1-1/4+1/4-1/7+...+1/(3N-2)-1/(3N+1))
=1/3(1-1/(3N+1)
=(1/3)*(3N/(3N+1))
=N/(3N+1)
|1-1/2|+|1/3-1/2|+|1/4-1/3|+.+|1/1000-1/999| |1-2/1|+|3/1-2/1|+|4/1-3/1|+.+|1000/1-999/1| 计算 ( 1+1/2)*(1-1/3)*（1+1/4)*(1-1/5)*.*(1+1/1000)*(1-1/1001） 1+2+3+4+.1000 1/1*2+1/2*3+1/3*4+.+1/998*999+1/999*1000 (1+1/2+1/3+...+1/2006)*(1/2+1/3+1/4+...1/2007)-(1+1/2+1/3+.. (1+1/2+1/3+1/4+1/5)*(1/3+1/4+1)-(1+1/3+1/4)*(1/2+1/3+1/4+1/5 奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4 1;(1-1/2^2)(1-1/3^2)(1-1/4^2)````````````(1-1/99^2)(1-1/100^ 提问题(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)×(1+1/2+1/ (1-1/2)*(1-1/3)*...*(1-1/1000) (1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于?