初二代数题计算：(1-1/2^2)(1-1/3^2)(1-1/4^2)···(1-1/19^2)(1-1/20^2)
2019-05-07
初二代数题
计算：(1-1/2^2)(1-1/3^2)(1-1/4^2)···(1-1/19^2)(1-1/20^2)
优质解答
(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/19)(1+1/19)(1-1/20)(1+1/20)
=(1/2)(3/2)(2/3)(4/3)...(18/19)(20/19)(19/20)(21/20)
=(1/2)*(21/20)
=21/40.
(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/19)(1+1/19)(1-1/20)(1+1/20)
=(1/2)(3/2)(2/3)(4/3)...(18/19)(20/19)(19/20)(21/20)
=(1/2)*(21/20)
=21/40.