Question

急：试求（1-1/2^2）(1-1/3^2)(1-1/4^2)……(1-1/10^2)的值

Answer 1

（1-1/2^2）(1-1/3^2)(1-1/4^2)……(1-1/10^2)
=(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)(3/4)(5/4)……(9/10)(11/10)
中间的都约分约掉了
=(1/2)*(11/10)
=11/20

Answer 2

解：原式=（1-1/2）X（1+1/2）X（1-1/3）X（1+1/3）…（1-1/9）X（1+1/9）X（1-1/10）
=1/2 X 3/2 X 2/3 X 4/3 … 8/9X10/9X9/10X11/10
=1/2X11/10
=11/20
这是我今天早上数学评价手册P52页上才写的 老师改过了 是对的0.0

Answer 3

（1-1/2^2）(1-1/3^2)(1-1/4^2)……(1-1/10^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4).....+(1+1/10)(1-1/10)
=3/2*1/2*4/3*2/3*5/4*3/4...11/10*9/10
=1/2*11/10
=11/20

Answer 4

（1-1/2^2）(1-1/3^2)(1-1/4^2)...(1-1/10^2)
=(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)(3/4)(5/4)...(9/10)(11/10)
=(1/2)(11/10)
=11/20

Answer 5

（1-1/2^2）(1-1/3^2)(1-1/4^2)……(1-1/10^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4).....+(1+1/10)(1-1/10)
=3/2*1/2*4/3*2/3*5/4*3/4...11/10*9/10
=1/2*11/10
=11/20