(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n)的值
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![(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n)的值](/uploads/image/z/12614425-25-5.jpg?t=%EF%BC%881%2B1%2F2%29%281%2B1%2F4%29%281%2B1%2F16%29%2B...%281%2B1%2F2%5E2n%29%E7%9A%84%E5%80%BC)
(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n)的值
(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n)的值
(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n)的值
(1+1/2)(1+1/4)(1+1/16)+...(1+1/2^2n) =2(1/2)(1+1/2)(1+1/4)(1+1/16)+……(1+1/2^2n) =2(1-1/2)(1+1/2)(1+1/4)(1+1/16)+……(1+1/2^2n) =2(1-1/4)(1+1/4)(1+1/16)+……(1+1/2^2n) =2(1-1/16)(1+1/16)……(1+1/2^2n) =…… =2(1-1/2^2n)(1+1/2^2n) =2(1-1/2^4n) =(2^4n-1)/2^(4n-1) (上式的分子是 2的4n次方-1 ,而分母是2的4n-1次方)