化简(1+1/2^2)(1+1/2^4 )(1+2/2^8)(1+2/2^16)
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解：
(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)
=(1-1/2^2)(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注：即上下同乘(1-1/2^2)
=(1-1/2^4)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注：平方差公式
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2^2)
=(1-1/2^16)(1+1/2^16)/(1-1/2^2)
=(1-1/2^32)/(1-1/2^2)
=(1-1/2^32)/(3/4)
=(4-1/2^30)/3
(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)
=(1-1/2^2)(1+1/2^2)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注：即上下同乘(1-1/2^2)
=(1-1/2^4)(1+1/2^4 )(1+1/2^8)(1+1/2^16)/(1-1/2^2) ...//注：平方差公式
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2^2)
=(1-1/2^16)(1+1/2^16)/(1-1/2^2)
=(1-1/2^32)/(1-1/2^2)
=(1-1/2^32)/(3/4)
=(4-1/2^30)/3
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