高校问答黑魂3卡露拉一套:初一数学计算题(关于平方差)
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(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)-1
注:1/2为二分之一,下类同 ^为乘方 注意过程详细 谢谢!!!
注:1/2为二分之一,下类同 ^为乘方 注意过程详细 谢谢!!!
{(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)}/1/2-1
={(1-1/2^2))(1+1/2^2)( 1+1/2^4)(1+1/2^8)}/1/2-1
={(1-1/2^4))( 1+1/2^4)(1+1/2^8)}/1/2-1
={(1-1/2^8))(1+1/2^8)}/1/2-1
={1-1/2^16}/1/2-1
=(1-1/65536)*2-1
=2-1/32768-1
==1-1/32768
=32767/32768
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)-1
=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)-1
=(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)-1
=(1-1/2^4)(1+1/2^4)(1+1/2^8)/(1-1/2)-1
=(1-1/2^8)(1+1/2^8)/(1-1/2)-1
=(1-1/2^16)*2-1
=2-1/2^15-1
=1-1/32768
=32767/32768
32767/32768
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