UC知道1/2*3+1/3*4+1*4*5.....1/99*100
来源：百度知道 编辑：UC知道 时间：2024/06/15 07:33:05
1/2*3=1/2-1/3
1/3*4=1/3-1/4
同理
1/99*100=1/99-1/100
把所有的式子相加得到1/2-1/100=49/100
答案是0.49
1/2*3+1/3*4+1*4*5.....1/99*100
=(1/2)-(1/3)+(1/3)-(1/4)+...+(1/99)-(1/100)
=(1/2)-(1/100)
=(50-1)/100
=49/100.
1/2*3+1/3*4+1*4*5.....1/99*100
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/98-1/99)+(1/99-1/100)
=1/2-1/3+1/3-1/4+1/4+...-1/99+1/99-1/100
=1/2-1/100=49/100
1/2*3 = 1/2 - 1/3
1/3*4 = 1/3 - 1/4
以此类推
原式=1/2 - 1/3 + 1/3 -1/4 +1/4 - ... +1/98 -1/99 + 1/99 -1/100
=1/2 - 1/100
=49/100
谢谢
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/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100)
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1+1/2+1/3+.....+1/2005][1/2+1/3+.......+1/2006]-[1/2+1/3+......+1/2005][1+1/2+1/3+1/2006]
(1-1/2-1/3-...-1/2001)*(1/2+1/3+...1/2002)-(1-1/2-1/3-...1/2002)*(1/2+1/3+...+1/2001)
1/1+1/2+1/3+1/4+。。。。+1/N 是多少