(1-1/2)(1+1/2)(1+1/4)(1+1/16) 求解
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小学方法解:
(1-1/2)(1+1/2)(1+1/4)(1+1/16)
=1/2×3/2×5/4×17/16
=(1×3×5×17)/(2×2×4×16)
=255/256
初中方法解:
(1-1/2)(1+1/2)(1+1/4)(1+1/16)
=[(1²-(1/2)²](1+1/4)(1+1/16)
=(1-1/4)(1+1/4)(1+1/16)
=[(1²-(1/4)²](1+1/16)
=(1-1/16)(1+1/16)
=1²-(1/16)²
=1-1/256
=255/256
(1-1/2)(1+1/2)(1+1/4)(1+1/16)
=1/2×3/2×5/4×17/16
=(1×3×5×17)/(2×2×4×16)
=255/256
初中方法解:
(1-1/2)(1+1/2)(1+1/4)(1+1/16)
=[(1²-(1/2)²](1+1/4)(1+1/16)
=(1-1/4)(1+1/4)(1+1/16)
=[(1²-(1/4)²](1+1/16)
=(1-1/16)(1+1/16)
=1²-(1/16)²
=1-1/256
=255/256
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