UC知道1/(2*1)+1/(3*2)......+1/(2008*2007)=
来源：百度知道 编辑：UC知道 时间：2024/09/19 16:21:59
1/(2*1)+1/(3*2)......+1/(2008*2007)=
=(1-1/2)+(1/2-1/3)+...+(1/2007-1/2008)
=1-1/2008
=2007/2008
1/(2*1)+1/(3*2)+......+1/(2008*2007)=
=(1/1-1/2)+(1/2-1/3)+......+(1/2007-1/2008)
=1/1-1/2008
=2007/2008
1/(2*1)+1/(3*2)+......+1/(2008*2007)=
=(1/1-1/2)+(1/2-1/3)+......+(1/2007-1/2008)
=1/1-1/2008
=2007/2008
1/(2*1)+1/(3*2)......+1/(2008*2007)=
=(1-1/2)+(1/2-1/3)+...+(1/2007-1/2008)
=1-1/2008
=2007/2008
此题记住形如1/ab都可表示为1/a-1/b(a<b)
1/(2*1)+1/(3*2)......+1/(2008*2007)=
1/1-1/2+1/2-1/3+......+1/2007-1/2008
=1-1/2008
=2007/2008
对
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
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+1/2+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...+2000
1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=?
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)