(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 23:14:19
(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)=?

(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)=?
(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)=?

(1-1/2²)(1-1/3²)(1-1/4²).(1-1/10²)=?
原式=(1+1/2)(1-1/2)(1+1/3)(1-1/3)****(1+1/10)(1-1/10)
=1/2*3/2*2/3*4/3******9/10*11/10
=1/2*11/10=11/20

(1-1/2²)(1-1/3²)(1-1/4²).........(1-1/10²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/10)(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4*……*9/10*11/10
=1/2*11/10
=11/20