(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)递等式简便计算.
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![(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)递等式简便计算.](/uploads/image/z/2683708-52-8.jpg?t=%281-1%2F2%29%C3%97%281%2B1%2F2%29%C3%97%281-1%2F3%29%C3%97%281%2B1%2F3%29%C3%97%281-1%2F4%29%C3%97%281%2B1%2F4%29%E9%80%92%E7%AD%89%E5%BC%8F%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97.)
(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)递等式简便计算.
(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)递等式简便计算.
(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)递等式简便计算.
解
(1-1/2)×(1+1/2)×(1-1/3)×(1+1/3)×(1-1/4)×(1+1/4)
=1/2×3/2×2/3×4/3×3/4×5/4
=1/2×(3/2×2/3)×(4/3×3/4)×5/4
=1/2×1×1×5/4
=5/8
=(1-1/4)*(1-1/9)*(1-1/16)
=3/4*8/9*15/16
=5/8