1/1*2*3+1/2*3*4+........+1/98*99*100=?
来源:百度知道 编辑:UC知道 时间:2024/06/06 02:02:01
1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]/2
1/1x2x3 + 1/2x3x4 +1/3x4x5 + … + 1/n(n+1)(n+2)
=[和1/n(n+1)-和1/(n+1)(n+2)]/2
=[1-1/(n+1)-1/2+1/(n+2)]/2
=1/4-1/2(n+1)(n+2)
1/n(n+2)=[1/n-1/(n+2)]/2
1/1x3 + 1/2x4 + 1/3x5 … + 1/n(n+2)
=[1+1/2-1/(n+1)-1/(n+2)]/2
=3/4-1/2(n+1)-1/2(n+2)
把数带入即可
3/4-1/2*99-1/2*100
1/1*2*3=1/2(1/1*2-1/2*3)
1/98*99*100=1/2(1/98*99-1/99*100)
1/1*2*3+1/2*3*4+........+1/98*99*100
=1/2(1/1*2-1/2*3+1/2*3-1/3*4+……+1/97*98-1/98*99+1/98*99-1/99*100)
=1/2(1/1*2-1/99*100)
=4949/19800
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+1/1+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)×
1/1+2 + 1/1+2+3 +....+ 1/1+2+3+....+100=