初二数学作业,求助
(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)
谢谢
参考答案:(1-1/2^2)(1-1/3^2)....(1-1/10^2)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×....×(1+1/10)×(1-1/10)
=3/2×1/2×4/3×2/3×....×11/10×9/10
=1/2×11/10
=11/20
(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)
谢谢
参考答案:(1-1/2^2)(1-1/3^2)....(1-1/10^2)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×....×(1+1/10)×(1-1/10)
=3/2×1/2×4/3×2/3×....×11/10×9/10
=1/2×11/10
=11/20