{2+1/2} {2^2+1/2^2} {2^4+1/2^4}{2^8+1/2^8}{2^16+1/2^16}

题目

答案

利用平方差公式
{2+1/2} {2^2+1/2^2} {2^4+1/2^4}{2^8+1/2^8}{2^16+1/2^16}
={2-1/2}{2+1/2} {2^2+1/2^2} {2^4+1/2^4}{2^8+1/2^8}{2^16+1/2^16}÷{2-1/2}
={2^2-1/2^2} {2^2+1/2^2} {2^4+1/2^4}{2^8+1/2^8}{2^16+1/2^16}÷{2-1/2}
={ 2^4-1/2^4}{2^4+1/2^4}{2^8+1/2^8}{2^16+1/2^16}÷{2-1/2}
={2^8-1/2^8}{2^8+1/2^8}{2^16+1/2^16}÷{2-1/2}
={2^16-1/2^16}{2^16+1/2^16}÷{2-1/2}
={2^32-1/2^32}÷{2-1/2}
=(2/3)(2^32-1/2^32)

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