1/1*2+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:2024/06/01 22:48:14
1/1*2+1/2*3+1/3*4+1/4*5……+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
中间正负抵消
=1-1/100
=99/100
1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
......
1/(99*100)=1/99-1/100
1/1*2+1/2*3+1/3*4+1/4*5……+1/99*100
=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100
方法1:
公式:y=1/n(n+1) n=1、2......99
y=1/n-1/(n+1)
=1-1/2+1/2-1/3+1/3-1/4......1/99-1/100
=1-1/100
=99/100
方法2:
1/1*2+1/2*3=2/3
1/1*2+1/2*3+1/3*4=3/4
1/1*2+1/2*3+1/3*4+1/4*5=4/5
...
1/1*2+1/2*3+1/3*4+1/4*5...+1/99*100=99/100
1/1*2+1/2*3+1/3*4+1/4*5……+1/99*100
=1/2+1/2-1/3+1/3-1/4+....-1/99+1/99-1/100
=1-1/100
=99/100
原式=1-1/100=99/100
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+----+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+~~~2005)=?
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)×
3/2=2+1/1*2=1/1+1/2
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)