Question

(1+二分之一)(1+2平方分之一)(1+2四次方分之一)(1+2的八次方分之一)(1+2的三十六次方分之一)题目如下

Answer 1

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)(1+1/2^32)

=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)(1+1/2^32) / (1-1/2)

=(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)(1+1/2^32) / (1-1/2)

=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)(1+1/2^32) / (1-1/2)

=(1-1/2^8)(1+1/2^8)(1+1/2^16)(1+1/2^32) / (1-1/2)

=(1-1/2^16)(1+1/2^16)(1+1/2^32) / (1-1/2)

=(1-1/2^32)(1+1/2^32) / (1/2)

=(1-1/2^64)×2

=2-1/2^63