计算:(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2) .
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计算:(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2) .
计算:(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2) .
计算:(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2) .
原式=:〔(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2)(1-1/2)〕/(1-1/2)
= [(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1-1/2^2)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1-1/2^4)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1+1/6^8)(1-1/2^8)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1-1/6^16)]/(1-1/2)
=[(1+1/2^32)(1-1/2^32)]/(1-1/2)
=(1-1/2^64)/(1/2)
=2-2/2^64
=2-1/2^63
=(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2)(1-1/2)/(1-1/2) 分号上下各乘一个(1-1/2),然后从后面开始不断地平方差公式
=(1+1/2^32)(1-1/2^32)/(1-1/2)
=(1-1/2^64)*2
=2-1/2^63
另外,你计算里面的(1+1/6^8) 6应该是2,考察平方差的灵活运用
1+1/2^32=(1-1/2^64)/(1-1/2^32)
...
1+1/2^2=(1-1/2^4)/(1-1/2^2)
1+1/2=(1-1/2^2)/(1-1/2)
原式=(1-1/2^64)/(1-1/2^32)*(1-1/2^32)/(1-1/2^16)*...*(1-1/2^4)/(1-1/2^2)*(1-1/2^2)/(1-1/2)
=(1-1/2^64)/(1-1/2)
=2-1/2^63
原式=:〔(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2)(1-1/2)〕/(1-1/2)
= [(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1-1/2^2)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1-1/2...
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原式=:〔(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1+1/2)(1-1/2)〕/(1-1/2)
= [(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1+1/2^2)(1-1/2^2)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1+1/6^8)(1+1/2^4)(1-1/2^4)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1+1/6^8)(1-1/2^8)]/(1-1/2)
=[(1+1/2^32)(1+1/2^16)(1-1/6^16)]/(1-1/2)
=[(1+1/2^32)(1-1/2^32)]/(1-1/2)
=(1-1/2^64)/(1/2)
=2-2/2^64
=2-1/2^63
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