(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.

(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