Question

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

Answer 1

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)