数学渗透法制教育教案:(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)=?

来源:百度文库 编辑:杭州交通信息网 时间:2024/05/02 13:19:56
写出简算过程。如答案满意,35点奖励。

(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)
=3/2*1/2*4/3*2/3*..........*10/9*8/9
=(3/2*4/3*5/4*..........*9/8*10/9)*(1/2*2/3*3/4*..........*7/8*8/9)
=10/2*1/9
=5/9

(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)
=(1+1/2)*(1+1/3)..........*(1+1/9)*
(1-1/2)*(1-1/3)..........*(1-1/9)
=(3/2*4/3*5/4*..........*9/8*10/9)*(1/2*2/3*3/4*..........*7/8*8/9)
=10/2*1/9
=5/9