初二数学作业,求助

来源:百度知道 编辑:UC知道 时间:2024/05/19 23:09:08
(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)

谢谢

(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)

=(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

用平方差公式展开
(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/10^2)
=1/2*3/2*2/3*4/3*3/4*5/4*...*9/10*11/10
=1/2*11/10
=11/20