UC知道(1-1/2*1/2)*(1-1/3*1/3)*......*(1-1/2007*1/2007)*(1-1/2008*1/2008)=?
来源：百度知道 编辑：UC知道 时间：2024/07/01 07:40:07
1-(1/n^2)=(n^2-1)/n^2=(n-1)(n+1)/n^2=[(n-1)/n][(n+1)/n]
原式=[(1/2)*(3/2)][(2/3)*(4/3)]*……[(2007/2008)*(2009/2008)]
=(1/2)*(2009/2008)
=2009/4016
(1-1/2*1/2)*(1-1/3*1/3)*......*(1-1/2007*1/2007)*(1-1/2008*1/2008)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/2007)(1+1/2007)(1-1/2008)(1+1/2008)
=1/2*3/2*2/3*4/3*...*2006/2007*2008/2007*2007/2008*2009/2008
=1/2*2009/2008
=2009/4016
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1+1/2+1+1/3+1+1/4+......+1/100=?
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
(1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2)
1/1+1/2+1/3+1/4+。。。。+1/N 是多少
1/1+1/2+1/3+1/4+......1/2002＝？
1-1/2+1/3-1/4+........1/99-1/100
求和Sn=1+(1+1/2)+(1+1/2+1/4)+....+[1+1/2+1/4.....+1/2^(n-1)]
数列 1+(1+1/2)+(1+1/2+1/4)+..............=?