UC知道(1-1/2)*(1-1/4)*(1-1/6)*...........*(1-1/10)解法
来源：百度知道 编辑：UC知道 时间：2024/06/24 10:45:20
简便解法,帮忙想想
(1-1/2)*(1-1/4)*(1-1/6)*...........*(1-1/10)
=1/2*3/4*5/6*7/8*9/10
=63/256.
=(1+1/2)*(1-1/2)*(1-1/4)*(1-1/6)*...........*(1-1/10)/(1+1/2)
=(1-1/20))/(1+1/2)
=19/30
有没有搞错,直接算嘛,1/2 * 3/4 * 5/6 * 7/8 * 9/10 = 63/256
解：
假设上式为S
S=（1-1/2)*(1-1/4)*(1-1/6)*...........*(1-1/10)
LnS=ln(1-1/2)+...+Ln(1-1/10)
=ln(1/2)+..+Ln(9/10)
=ln2-ln1+Ln4-ln3+Ln6-ln5+ln8-ln7+ln10-ln9
=ln3840/945
=Ln768/189=ln256/315
S=256/315
(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+1/1+2+1/1+2+3+...+1/1+2+3...+2000
1+1/1+2+1/1+2+3.........+1/1+2+3.....100
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)
(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+1/2+1+1/3+1+1/4+......+1/100=?