利用平方差公式计算:(1+1/2)(1+1/4)(1+1/16)(1+1/256)

问题描述:

利用平方差公式计算:(1+1/2)(1+1/4)(1+1/16)(1+1/256)

(1+1/2)(1+1/4)(1+1/16)(1+1/256)两个括号之间是乘法吗?

原式×(1-1/2)
=(1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=(1-1/4)(1+1/4)(1+1/16)(1+1/256)
=(1-1/16)(1+1/16)(1+1/256)
=(1-1/256)(1+1/256)=1/65536
原式=(1/65536 )/(1-1/2)
=1/32768
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(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=2*(1/2)*(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=2*(1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)
=2*(1-1/4)(1+1/4)(1+1/16)(1+1/256)
=2*(1-1/16)(1+1/16)(1+1/256)
=2*(1-1/256)(1+1/256)
=65535/32768