(1+2平方分之一)(1+2四次方分之一)````(1+2的2n次方分之一)
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  • (1+(1/2)^2)(1+(1/2)^4)……(1+(1/2)^2n)

    =(1-(1/2)^2)(1+(1/2)^2)(1+(1/2)^4)……(1+(1/2)^2n)/(1-(1/2)^2)

    =(1-(1/2)^2)(1+(1/2)^2)(1+(1/2)^4)……(1+(1/2)^2n)/(3/4)

    (现在用平方差公式(a+b)(a-b)=a^2-b^2)

    =(1-(1/2)^4)(1+(1/2)^4)……(1+(1/2)^2n)/(3/4)

    ……

    =(1-(1/2)^2n)(1+(1/2)^2n)/(3/4)

    =4*(1-(1/2)^4n)/3

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